## Cyclical Fiscal Multipliers: Policy Mix and Financial Friction Puzzle — Working Paper No. WP/2025/108

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---

### Main research question and methodological advances
- Research question:
  - How do fiscal multipliers evolve during a recession, particularly when considering the potential influence of higher-order non-linearities that are often overlooked by aggregate time series models?
- Model innovations:
  - Extends the Time-Varying Parameter Vector Autoregression (TVP-VAR) model of Belmonte et al. (2014) to estimate a series of time-varying fiscal multipliers.
  - Incorporates a decision mechanism that adjusts the degree of time variation in parameters.
  - Applies a Tobit prior to regulate the extent of time variation and a Lasso prior to variances (following Eisenstat et al. (2016)).
  - Extends the VAR lag polynomial to four lags (Blanchard and Perotti (2002)) to capture delayed effects across four quarters.
  - Estimates on stationary series in de-trended levels using Hamilton (2018)’s linear projection method to avoid re-scaling bias.

### Data, estimation, and identification
- Sample and data:
  - Sample: Q1 1948 to Q2 2018.
  - Variables: government expenditure (G_t), tax revenue net of transfers (NT_t), GDP (Y_t), all in real per capita terms.
- Estimation:
  - Bayesian Gibb’s sampler with 150,000 iterations.
  - Burn-in: 100,000 iterations removed.
  - Posterior approximation: every 25th draw of remainder used.
  - var([u_t v_t θ_t]′) matrix assumed diagonal (Primiceri (2005)).
  - Uninformative priors to preserve comparability across subsamples.
- Identification:
  - Mixture of sign restrictions with short-term zero restrictions following Rubio-Ramirez et al. (2010) and Binning (2013); short-term zero restrictions follow Blanchard and Perotti (2002).
  - Identification summarized in the source notation: Z_t = ( ε^G_t  ε^T_t  ε^Y_t ; G_0 +0 0 NT 0 × + × Y_0 × − + ).
  - Sign restrictions used to avoid Cholesky pitfalls when VAR includes tax revenues as endogenous.

### Definitions of multipliers computed
- Cumulative multiplier:
  - K_sum_t = Σ_H h=0 f_{y t+h} / Σ_H h=0 f_{g t+h}
- Impact multiplier:
  - K_imp_t = f_{y t}
- Notation:
  - f_{y t+h} denotes the output response at horizon h to a fiscal shock at time t; f_{g t+h} denotes the fiscal variable counterpart.
- Note:
  - Cumulative multiplier definition follows Ramey and Zubairy (2018) and tends to provide lower multiplier values than alternative definitions.

### Key empirical findings on drivers of multiplier variation
- Non-constant relationship with business cycle:
  - Relationship between multipliers and business cycle stage is not constant over time.
  - Post-WWII sample splits into two subperiods:
    - 1949 to the late 1980s: counter-cyclical fiscal expenditure multipliers (multipliers higher in recessions).
    - Since the late 1980s: pro-cyclical fiscal multipliers (multipliers larger in expansions).
- Role of policy mix:
  - Higher multipliers tend to occur during fiscally-led policy mixes (active fiscal policy, passive monetary policy).
  - Reduced average multiplier size since the 1980s attributed to shift toward a monetary-led policy mix, notably during Paul Volcker’s disinflationary effort.
  - Comparative 10-quarter cumulative multiplier averages:
    - Pre-Volcker period: 0.6 (this estimate) versus 1.2-1.6 range in Leeper et al. (2017).
    - Post-Volcker period: 0.1 (this estimate) versus 0.5-0.7 range in Leeper et al. (2017).
- Variation driven by policy shifts rather than recessions per se:
  - Elevated multipliers in recessions of late 1960s–early 1980s likely driven by aggressive fiscal policies (unfunded spending or tax cuts) rather than inherent recession feature.
- Financial frictions and recent recessions:
  - Some post-2000s recessions, including the global financial crisis, show decreased multipliers—contradicting the view that multipliers generally rise during downturns.
  - Particularly low government spending multiplier during the global financial crisis highlighted.
  - Evidence suggests the role of financial frictions in the U.S. economy may have shifted, reducing potency of fiscal stimulus when household debt and financial constraints were elevated.
  - Structural-model consistency: financial frictions can lower tax multipliers and attenuate government spending multipliers (e.g., Ghiaie and Rouillard (2022)).

### Robustness checks and anticipation
- Forecast-control extension:
  - Incorporates professional forecasts into TVP-VAR (Berg (2015)) to control for previous quarter’s forecast and remove anticipated components.
  - Forecast-controlled extension estimated on 1966Q4—2010Q3 using Survey of Professional Forecasters for government spending growth forecasts.
- Finding:
  - Accounting for policy anticipation (controlling for only the previous quarter’s forecast) does not alter main qualitative results.
  - Impact multipliers increase under forecast control: Impact = 1.23 (unanticipated US$1 discretionary government expenditure shock raises output by an average of US$1.23).
  - All cumulative multipliers are lower in the forecast-controlled extension than baseline, but core structural break (pre- vs post-late 1980s) persists.
- Anticipation diagnostic (baseline vs SPF forecasts):
  - corr = 0.289958
  - R̄2 = 0.0523002
  - s.e. = 0.0221407
  - R2 reported in text: 0.0408 (forecasters predict only a small fraction of the variance).

### Exact multiplier statistics reported (baseline and forecast-controlled unanticipated-shock extension)
- Baseline descriptive statistics (Table 1, preserved as presented):
  - Impact: Average = 0.97***; Min date = 2017Q4 value 0.93***; Max date = 1960Q4 value 1.03***.
  - Sum (1-year): Average = 0.89**; Min date = 2011Q1 value 0.65*; Max date = 1958Q1 value 1.38**.
  - Sum (2-year): Average = 0.83 2014Q4; Min date = 0.05 1982Q4; Max date = 2.23* (values and dates appear in the source as "0.832014Q40.051982Q42.23 ∗").
  - Sum (4-year): Average = 0.78 2009Q2; Min = -0.64 1958Q1; Max = 2.29*.
  - Sum (5-year): Average = 0.77 2014Q4; Min = -0.33 1958Q1; Max = 2.35*.
  - Significance notation: *p <0.32, **p <0.1, ***p <0.05.
- Forecast-controlled (unanticipated discretionary shocks) descriptive statistics (Table 2):
  - Impact: Average = 1.23***; Min date = 1984Q2 value 1.09*; Max date = 1975Q2 value 1.37***.
  - Sum (1-year): Average = 0.36 1987Q1; Min date = 0.02 1975Q1; Max date = 0.80.
  - Sum (2-year): Average = 0.29 2009Q1; Min date = -0.57 1975Q1; Max date = 0.95.
  - Sum (4-year): Average = 0.36 2008Q4; Min date = -0.57 1974Q4; Max date = 0.85.
  - Sum (5-year): Average = 0.32 2007Q2; Min date = -0.39 1975Q1; Max date = 0.81.
  - Significance notation: *p <0.32, **p <0.1, ***p <0.05.

### Identification strategy and implementation (Appendix D summary)
- Variable set and concerns:
  - Key endogenous variables: G_t, NT_t, Y_t (real per capita).
  - Net taxes defined per Blanchard and Perotti (2002).
  - Concern: small set of endogenous variables may raise non-fundamentality/omission concerns (Chung and Leeper (2009); Leeper et al. (2013); Mertens and Ravn (2010)); alternative specification conditions on professional forecasters’ projections to align information sets.
  - Omission risk: excluding public debt limits ability to capture role of these omitted variables in transmission.
- Detrending and stationarity:
  - Hamilton (2018) linear projection method used to obtain stationary cyclical components in levels; recommended h = 8 and lag polynomial order 4 for quarterly data.
  - Hamilton’s method avoids rescaling bias and produces multipliers (not elasticities).
- Identification details:
  - Mixture of sign and short-term zero restrictions following Binning (2013) and Blanchard and Perotti (2002).
  - Assumptions (as in source): α_gy_t = 0; β_gt = 0; α_ty_t positive; α_yt_t negative.
  - Structural system under these assumptions represented in matrix form with time-varying coefficients c_ij_t and impact matrix Z_t as preserved in the source.
  - Short-term zero and sign restrictions permit contemporaneous output response to a tax shock to be restricted negative while allowing other contemporaneous relationships to be estimated.
- Estimation machinery:
  - State-space TVP-VAR with stochastic volatility:
    - Y_t = X_t α + X_t Φ ̃ Ω^(1/2) γ_t + Σ_t u_t, u_t ∼ N(0, I)
    - γ_t = γ_{t−1} + v*_t, v*_t ∼ N(0, I)
    - log(σ_t) = log(σ_{t−1}) + θ_t, θ_t ∼ N(0, W)
  - Two-part sampler:
    - Model 1 (linear Gaussian) solved via Carter and Kohn (1994).
    - Model 2 (stochastic volatility) solved via Kim et al. (1998) (mixture of log-normals approximation).
  - Priors and Tobit/Lasso structure preserved as specified in source.
  - Gibbs sampler steps enumerated and implemented as in source.

### Fiscal-monetary policy mix evidence and interpretation
- Theoretical regimes:
  - Fiscally-led: central bank largely unresponsive to inflation; fiscal stimulus perceived as unfunded; multipliers larger.
  - Monetary-led: central bank prioritizes inflation stabilization; fiscal stimulus perceived as funded; multipliers smaller or even contractionary.
  - Conflicting mix: monetary tightening and fiscal non-stabilization can raise debt-to-GDP and interest payments.
- Empirical linkage using Bianchi and Ilut (2017) regime probabilities (1954Q4–2009Q3):
  - Multiplier values notably higher pre-Volcker (before 1979Q3) when fiscally-led mix probabilities were high.
  - Consistent decline in multipliers during Paul Volcker’s tenure (1979Q3–1987Q3) as regime shifted to monetary-led.
  - Post-Volcker (after 1987Q3) multipliers further diminish with sustained monetary-led probabilities.
- Term spread evidence:
  - Before 1990, past yield spreads (five term spreads with eight lags in first differences) explain changes in 2-year cumulative multiplier; fit deteriorates post-1990.
  - Interpretation: slope of yield curve is forward-looking predictor of multiplier shifts pre-1990, consistent with monetary-policy-related explanation for structural break.

### The financial friction puzzle
- Core puzzle:
  - Contrary to prior findings, multipliers did not consistently increase in recessions of 1990-1991, 2001, and 2007-2009; during the global financial crisis multipliers declined sharply.
- Evidence:
  - 2008 crisis: dramatic widening of credit spreads, slowdown in credit growth, ratio of private debt to income more than doubled relative to earlier sample periods.
  - Historical relationship: earlier positive relationship between fiscal multipliers and credit spreads; in 2000s–10s relationship appears to reverse (higher credit spreads associated with lower multipliers).
- Interpretation challenges:
  - Forward-looking nature of credit and term spreads introduces endogeneity concerns.
  - Global financial integration and cross-border amplification complicate single-country attribution.
- Suggested mechanisms and references:
  - Increased financial frictions and household indebtedness can weaken fiscal effectiveness (Gilchrist and Zakrajšek (2012); Mian and Sufi (2010); Andrés et al. (2015); Justiniano et al. (2015)).
  - Structural-model evidence consistent with findings that financial frictions can lower tax multipliers and attenuate spending multipliers (Canzoneri et al. (2016); Ghiaie and Rouillard (2022)).

### Conclusions and suggested future research
- Key takeaways:
  - Introduced government expenditure multipliers that vary across business cycle phases using a TVP-VAR framework; state-dependence is time-varying and exhibits a structural break in the 1980s.
  - Documented that average multipliers became significantly smaller since the 1980s, driven primarily by shifts in the fiscal-monetary policy mix rather than recessions per se.
  - Identified a novel transmission puzzle: financial frictions historically amplified multipliers but this relationship reversed in the 21st century, notably during the global financial crisis.
- Suggested future directions (preserved from source):
  - Use less flexible but more efficient estimators (e.g., approaches similar to Ramey and Zubairy (2018); Bernardini and Peersman (2018)) to validate relationships.
  - Expand fiscal VAR to include additional variables such as public debt and inflation or apply framework to broader set of advanced economies.
  - Investigate changing role of financial frictions within theoretical models (e.g., Canzoneri et al. (2016)) to explain negative correlation between multipliers and financial frictions during the Dot-com recession and global financial crisis.
  - Examine evolving fiscal-monetary policy mixes, including unconventional monetary policies (e.g., Bi and Traum (2023)).

*Italic: Source: wpiea2025108-print-pdf - 6.1    Drivers; Appendix D; related sections, canonical PDF https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025108-print-pdf.pdf*

### 6.1    Drivers .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  

### 6.1    Drivers

### Main research question and methodological advances
- Research question: How do fiscal multipliers evolve during a recession, particularly when considering the potential influence of higher-order non-linearities that are often overlooked by aggregate time series models?
- Model innovations:
  - Extends the Time-Varying Parameter Vector Autoregression (TVP-VAR) model developed by Belmonte et al. (2014) to estimate a series of time-varying fiscal multipliers.
  - Incorporates a decision mechanism that adjusts the degree of time variation in parameters.
  - Applies a Tobit prior to regulate the extent of time variation and a Lasso prior to variances, following Eisenstat et al. (2016).
  - Extends the VAR lag polynomial to four lags, in line with Blanchard and Perotti (2002), to capture delayed effects across the four quarters of a fiscal year.
  - Estimates the model on stationary series in de-trended levels using Hamilton (2018)’s linear projection method to avoid re-scaling bias.

### Data, estimation, and identification
- Sample: Q1 1948 to Q2 2018.
- Estimation details:
  - Bayesian Gibb’s sampler with 150,000 iterations.
  - Burn-in period of 100,000 iterations removed.
  - Every 25th draw of the remainder is used to approximate the posterior density.
  - var([u_t v_t θ_t]′) matrix assumed diagonal, following Primiceri (2005).
  - Uninformative priors are used to preserve comparability across subsamples and avoid imposing pre-regime priors on later regimes.
- Identification scheme:
  - Combines sign restrictions with short-term zero restrictions following Rubio-Ramirez et al. (2010) and the implementation strategy of Binning (2013).
  - Short-term zero restrictions follow Blanchard and Perotti (2002).
  - Identification summarized as:
    Z_t = ( ε^G_t  ε^T_t  ε^Y_t ; G_0 +0 0 NT 0 × + × Y_0 × − + )
    (as presented in the original specification, where ε_G_t is the structural government expenditure shock, ε_T_t is the structural tax shock, and ε_Y_t is the structural output shock).
  - Sign restrictions avoid pitfalls of Cholesky factorization when the VAR includes tax revenues as endogenous.

### Definitions of multipliers computed
- Cumulative multiplier:
  - K_sum_t = Σ_H h=0 f_{y t+h} / Σ_H h=0 f_{g t+h}
- Impact multiplier:
  - K_imp_t = f_{y t}
- f_{y t+h} denotes the output response at horizon h to a fiscal shock at time t; f_{g t+h} denotes the fiscal variable counterpart.
- Note: The cumulative multiplier definition follows Ramey and Zubairy (2018) and tends to provide lower multiplier values than alternative definitions.

### Key empirical findings on drivers of multiplier variation
- Non-constant relationship with business cycle:
  - The relationship between multipliers and the business cycle stage is not constant over time.
  - Post-WWII sample splits into two subperiods:
    - 1949 to the late 1980s: counter-cyclical fiscal expenditure multipliers (multipliers higher in recessions).
    - Since the late 1980s: pro-cyclical fiscal multipliers (multipliers larger in expansions).
- Role of policy mix:
  - Higher multipliers tend to occur during fiscally-led policy mixes (active fiscal policy, passive monetary policy).
  - Reduced average multiplier size since the 1980s is attributed to a shift toward a monetary-led policy mix, notably during the Federal Reserve’s prolonged disinflationary effort under Paul Volcker.
  - Findings are consistent with Leeper et al. (2017); Bianchi and Ilut (2017); Bianchi et al. (2023).
- Variation driven by policy shifts rather than recessions per se:
  - Elevated multipliers in recessions of the late 1960s, 1970s, and early 1980s likely driven by more aggressive fiscal policies (e.g., unfunded increases in government spending or tax cuts) rather than an inherent feature of recessions.
  - This challenges the claim that multipliers are consistently higher during recessions (e.g., Auerbach and Gorodnichenko (2012)).
- Recent decades and financial frictions:
  - Some recent recessions (post-2000s), including the global financial crisis, show decreased multipliers—contradicting the view that multipliers generally rise during downturns.
  - The particularly low government spending multiplier during the global financial crisis is highlighted.
  - Examination across subsamples suggests the role of financial frictions in the U.S. economy may have shifted in recent years, reducing the potency of fiscal stimulus when household debt and financial constraints were elevated.
  - This reverses the earlier-sample relationship where financial frictions tended to enhance multipliers (e.g., Carrillo and Poilly (2013); Canzoneri et al. (2016)).
  - Empirical results align with structural-model findings (e.g., Ghiaie and Rouillard (2022)) that financial frictions can lower tax multipliers and, consistent with this paper’s evidence, can attenuate government spending multipliers.

### Robustness checks and anticipation
- Incorporates professional forecasts into TVP-VAR following Berg (2015) to control for the previous quarter’s forecast and remove anticipated components of structural shocks.
- Finding: Accounting for policy anticipation (controlling for only the previous quarter’s forecast) does not alter the main results.

### Literature positioning and contributions
- Claimed first in the literature to present state-dependent fiscal multipliers in a TVP-VAR framework while:
  - Extending the lag polynomial to fourth order,
  - Detrending using Hamilton (2018)’s linear projection method,
  - Not discarding unstable draws of the lag polynomial in Gibb’s sampling,
  - Estimating the model in levels.
- Fills two gaps:
  - Estimates government expenditure multipliers that depend on the business cycle stage using a Bayesian TVP model.
  - Investigates whether the state-dependent nature of the public expenditure multiplier is stable across the post-WWII period in the U.S.
- Contrasts with earlier findings:
  - Challenges models that find no relationship between multipliers and business cycle stage or that assume a fixed relationship (e.g., Ramey and Zubairy (2018); Pereira and Lopes (2014); Berg (2015); Afonso et al. (2018); Iwata and IIboshi (2023)).
  - Suggests that prior inability to detect state-dependence may stem from common modeling choices (e.g., limited lag order, detrending choices, discarding unstable draws).

### Implications for interpretation of multipliers
- The state-dependence of multipliers can evolve over time due to policy regime shifts (fiscal vs. monetary leadership), changes in the share of unfunded government expenditure, and shifts in financial landscape and household indebtedness.
- Empirical strategy that allows time variation and higher lag order can reveal regime-ordered changes in multipliers that fixed-regime or limited-lag models may miss.

*Italic: Source: wpiea2025108-print-pdf - 6.1    Drivers, canonical PDF https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025108-print-pdf.pdf*

### Appendix D presents an elaborate explanation of the identification strategy.

### wpiea2025108-print-pdf - Appendix D presents an elaborate explanation of the identification strategy.

### Identification strategy and variable set
- The TVP-VAR model incorporates key variables: government expenditure (Gt), tax revenue net of transfer payments (NTt), and GDP (Yt), all expressed in real per capita terms.
- Net taxes follow the definition of Blanchard and Perotti (2002) (detailed definitions are presented in Appendix B).
- The model estimates structural shocks using a mixture of sign and zero restrictions and produces state-dependent IRFs.
- Concern noted: the relatively small set of endogenous variables may raise non-fundamentality concerns because shocks are conditioned on a limited information set (references: Chung and Leeper (2009), Leeper et al. (2013), Mertens and Ravn (2010)).
- To address limited information sets, an alternative specification conditions the VAR on professional forecasters’ projections to align the model’s information set with that of market agents.
- Omission risk: excluding key state variables such as public debt limits the ability of estimated IRFs to capture the role of these omitted variables in the transmission of discretionary fiscal shocks.

### Data preparation and stationary transformation
- GDP, government expenditure, and net taxes are non-stationary time series; estimations in levels may lead to spurious results, while detrending may remove valuable information.
- The study adopts Hamilton (2018)’s linear projection method to obtain stationary cyclical components centered around zero.
  - Hamilton (2018) produces stationary series in levels similar to the Hodrick-Prescott filter but avoids creating artificial correlations.
  - Using Hamilton’s method means the TVP-VAR estimated on cyclical components in levels directly produces multipliers (not elasticities) and avoids the rescaling bias identified by Ramey and Zubairy (2018).
- Figure 1 (described) presents the stationary transformations of real per capita government expenditure (A), taxes net of transfers (B), GDP (C) over NBER recession dates obtained via Hamilton’s linear projection method.
- Sample and sources:
  - Baseline TVP-VAR run on the 1948Q1–2018Q2 sample.
  - Assumed four lags and no intercept terms.
  - Data obtained from the Bureau of Economic Analysis and the Federal Reserve Economic Database.
  - Fiscal variables and GDP taken from the latest release of the national income and product accounts’ tables.
- In projecting multiplier changes on interest rate spreads, the study obtains five interest rate spreads from the federal reserve economic database: (i) 10-year treasury constant maturity minus federal funds rate, (ii) 5-year treasury constant maturity minus federal funds rate, (iii) 1-year treasury constant maturity minus federal funds rate, (iv) 6-month treasury bill minus federal funds rate, and (v) 3-month treasury bill minus federal funds rate.

### Model specification and comparisons
- Baseline: TVP-VAR estimated on Hamilton (2018) detrended real per capita series in levels; four lags; no intercepts.
- Comparison model: VAR of Blanchard and Perotti (2002) used as point of comparison and related to earlier time-varying fiscal VAR studies (Pereira and Lopes (2014), Berg (2015)).
- The TVP-VAR accommodates shifts in both the lag polynomial and the variance-covariance matrix over time, addressing potential issues from estimating linear VARs on data from distinct regimes (Ascari et al. (2023) argument).
- An extension conditions the VAR on professional forecasted government spending growth (Survey of Professional Forecasters) to extract the unanticipated component of fiscal shocks; this extension is estimated on 1966Q4—2010Q3.

### Main empirical findings on government expenditure multipliers
- State dependence:
  - The TVP-VAR framework provides estimates of state-dependent IRFs; median IRFs are the focus to minimize unstable draws.
  - Time variation is substantial across the post-WWII US timeline and depends on the stage of business cycles.
- Impact (short-run) response:
  - Output response on impact remains approximately close to unity throughout the sample — an additional US$1 of government expenditure increases aggregate demand by roughly the same amount in the same quarter (Keynesian accounting effect).
- Long-term heterogeneity:
  - Majority of heterogeneity in IRFs emerges at distant horizons; medium-to-long-term crowding-in and crowding-out effects vary over time and by business cycle stage.
- Structural break and time subperiods:
  - Relationship between business cycle stage and the fiscal multiplier undergoes a structural break in the 1980s.
  - Post-WWII sample can be divided into two parts:
    - From sample start to the late 1980s.
    - From the late 1980s to the modern-day.
  - Highest multiplier values consistently occur during recessions as defined by the NBER, but only in those preceding the late 1980s.
  - During the last two recessions of the sample period, the relationship inverts and the 2-year cumulative multiplier declines.
- Predictability by interest rate spreads:
  - Using eight lags of the five term spreads in first differences (because TVP-VAR coefficients are random walks), past yield spreads explain changes in the 2-year cumulative multiplier before 1990 but not thereafter.
  - Fit improves when limiting estimation to observations before 1990.
  - Interpretation: the slope of the yield curve (term spread) is a forward-looking predictor of multiplier shifts pre-1990, suggesting a monetary-policy-related explanation for the structural break.

### Shock anticipation, forecast control, and robustness
- Anticipation concern:
  - Structural shocks estimated by a TVP-VAR may be anticipated by market agents because econometricians have more limited information; anticipated elements bias IRFs (Mertens and Ravn, 2010).
  - Figure 5 scatter: structural shocks from baseline vs. government expenditure growth forecasts (SPF) shows correlation and regression diagnostics:
    - corr = 0.289958
    - R̄2 = 0.0523002
    - s.e. = 0.0221407
    - R2 reported in text: 0.0408 (forecasters predict only a small fraction of the variance).
- Methods to address anticipation:
  - Narrative shock series (unanticipated events) — valuable but often specific to military or unique events and not representative of overall government expenditure types.
  - Forecast-control approach (Auerbach and Gorodnichenko (2012); Berg (2015)) — incorporates professional forecasts to remove anticipated components.
- Implementation in this study:
  - The extension controls for the current forecast made in the previous quarter (forecasted growth rates used rather than levels).
  - Forecasts of government revenues and output are excluded due to data limitations and the belief that output shocks are less anticipated than fiscal policy shocks.
  - Estimation performed on 1966Q4—2010Q3 for the forecast-controlled TVP-VAR.
- Effects of controlling for professional forecasts (summary of changes relative to baseline):
  - Impact multipliers increase: an unanticipated US$1 discretionary government expenditure shock raises output by an average of US$1.23 (Impact = 1.23).
  - All cumulative multipliers are lower than in the baseline model (see Table 2 for exact values).
  - Maximum and minimum dates/values of estimated multipliers shift to different dates, but core qualitative conclusion remains: highest multipliers occur in the earlier part of the sample (before the late 1980s); 2-year, 4-year, and 5-year cumulative multipliers reach lowest levels around the global financial crisis.
- Conclusion on anticipation: Controlling for policy anticipation does not overturn the baseline finding that the relationship between the stage of the business cycle and the government expenditure multiplier is not constant over time.

### Exact multiplier statistics reported (baseline and unanticipated-shock extension)
- Table 1 (baseline descriptive statistics for estimated multiplier series):
  - Impact: Average = 0.97***; Min date = 2017Q4 value 0.93***; Max date = 1960Q4 value 1.03***.
  - Sum (1-year): Average = 0.89**; Min date = 2011Q1 value 0.65*; Max date = 1958Q1 value 1.38**.
  - Sum (2-year): Average = 0.83 2014Q4; Min date = 0.05 1982Q4; Max date = 2.23* (values and dates appear in the source as "0.832014Q40.051982Q42.23 ∗" — preserved as presented in the source).
  - Sum (4-year): Average = 0.78 2009Q2; Min = -0.64 1958Q1; Max = 2.29*.
  - Sum (5-year): Average = 0.77 2014Q4; Min = -0.33 1958Q1; Max = 2.35*.
  - Significance notation: *p <0.32, **p <0.1, ***p <0.05 (preserved as in source).
- Table 2 (descriptive statistics for estimated multiplier series: unanticipated discretionary shocks, forecast-controlled extension):
  - Impact: Average = 1.23***; Min date = 1984Q2 value 1.09*; Max date = 1975Q2 value 1.37***.
  - Sum (1-year): Average = 0.36 1987Q1; Min date = 0.02 1975Q1; Max date = 0.80.
  - Sum (2-year): Average = 0.29 2009Q1; Min date = -0.57 1975Q1; Max date = 0.95.
  - Sum (4-year): Average = 0.36 2008Q4; Min date = -0.57 1974Q4; Max date = 0.85.
  - Sum (5-year): Average = 0.32 2007Q2; Min date = -0.39 1975Q1; Max date = 0.81.
  - Significance notation: *p <0.32, **p <0.1, ***p <0.05 (preserved as in source).

### Key interpretive conclusions
- Short-run (impact) government expenditure effect is persistently near one dollar of output per US$1 of government expenditure.
- The potency of discretionary government expenditure in stimulating output fell sharply after the 1980s, with pronounced decreases in 1-year and cumulative multipliers beginning in the 1980s and especially after the global financial crisis.
- The highest multiplier values are concentrated in recessions before the late 1980s; after the late 1980s the relationship between multiplier and business cycle stage inverts for the most recent recessions.
- Term spreads (yield curve slope) predict multiplier shifts pre-1990 but not post-1990, suggesting a structural break potentially tied to changes in monetary policy and expectation formation.
- Controlling for professional forecasts (removing anticipated components) increases impact multipliers (Impact = 1.23) but results still show time-varying, state-dependent multipliers and the same qualitative structural break across the 1980s.

*Source: Appendix D and related sections of the provided PDF content.*

### 6.1    Drivers

### 6.1    Drivers

### Key arguments and overview
- The estimated fiscal multiplier series during the post-WWII period exhibits significant variation; existing literature does not fully explain cyclical patterns in post-1980s estimates.
- Two primary arguments advanced:
  - A connection between average multiplier size and fiscal-monetary interactions: multipliers tend to be larger during fiscally-led policy mix periods than during monetary-led regimes.
  - A new empirical puzzle: in some recent recessions multipliers decline rather than rise, potentially linked to changing roles of financial frictions.

### Findings on historical variation
- Peaks in fiscal multipliers during earlier U.S. recessions likely reflect shifts in the policy mix (from conflicting to fiscally-led), amplifying government expenditure multipliers during downturns.
- Post-1980s estimates show smaller average multipliers and cyclical behavior not explained solely by recessions.

### Implication
- Additional or evolving factors (beyond those emphasized in prior studies) have influenced multiplier fluctuations, requiring further investigation into policy mix dynamics and financial frictions.

---

### Fiscal multiplier and the fiscal-monetary policy mix (Section 6.2)

- Theoretical regimes described:
  - Fiscally-led policy mix: central bank largely unresponsive to inflation, government does not adhere to a fiscal rule stabilizing debt-to-GDP; fiscal policy active, monetary policy passive. Fiscal stimulus perceived as unfunded (non-Ricardian), boosting private spending while inflation expectations rise and nominal interest rates remain low; inflation reduces real debt value and stabilizes debt-to-GDP.
  - Monetary-led policy mix: central bank prioritizes inflation stabilization, fiscal policy generates surpluses to keep debt-to-GDP near a target; fiscal stimulus perceived as funded (Ricardian equivalence), private demand response muted; debt-to-GDP and inflation expectations remain stable.
  - Conflicting policy mix: central bank fights inflation while fiscal authority does not prioritize debt stabilization; primary deficits fuel inflationary pressures and force higher real interest rates, raising debt-to-GDP and interest payments.

- Empirical linkage using regime probabilities from Bianchi and Ilut (2017) (1954Q4 to 2009Q3, three regimes):
  - Three key observations from Figure 8:
    - Multiplier values notably higher during the pre-Volcker era (before 1979Q3), a period with high probabilities of a fiscally-led policy mix.
    - A consistent decline in multiplier values occurs during Paul Volcker’s tenure (1979Q3-1987Q3), aligning with initial high conflict regime probabilities followed by a shift to a monetary-led regime.
    - In the post-Volcker period (after 1987Q3), fiscal multipliers further diminish, corresponding with sustained high probabilities of a monetary-led policy mix.

- Comparative estimates and deviations from structural models:
  - The model’s 10-quarter cumulative multiplier average:
    - Pre-Volcker period: 0.6 (our estimate) versus 1.2-1.6 range in Leeper et al. (2017).
    - Post-Volcker period: 0.1 (our estimate) versus 0.5-0.7 range in Leeper et al. (2017).
  - Our estimates indicate unanticipated shocks can be contractionary (negative multipliers) in the monetary-led regime, deviating from some literature (e.g., Ascari et al. (2023)).

- Role of term spreads and policy shifts:
  - Before Volcker, negative term spreads typically preceded policy shifts and were associated with increases in future multipliers; this relationship disappears in the post-Volcker era.
  - Term spread dynamics, political pressure on the Federal Reserve (Drechsel, 2024), and brief disinflationary efforts contributed to shifts back to accommodative monetary stances and fiscally-led mixes in earlier decades, explaining earlier recession-associated multiplier peaks.

---

### The financial friction puzzle (Section 6.3)

- Core puzzle:
  - Contrary to prior findings that multipliers rise during recessions, the model shows multipliers did not consistently increase in recessions of 1990-1991, 2001, and 2007-2009; in the global financial crisis multipliers declined sharply.
  - The sharp decline during the global financial crisis remains an unresolved issue tied to financial frictions.

- Evidence and mechanisms:
  - The 2008 crisis led to a dramatic widening of credit spreads, a substantial slowdown in credit growth, and the ratio of private debt to income more than doubled relative to earlier sample periods.
  - Empirical literature (Gilchrist and Zakrajšek (2012); Mian and Sufi (2010); Andrés et al. (2015); Justiniano et al. (2015)) suggests increased financial frictions and high household debt can weaken fiscal policy effectiveness.
  - Figure 11 segmenting four periods (a) 1950s-60s; (b) 1970s; (c) 1980s-90s; (d) 2000s-10s shows:
    - Historically positive relationship between fiscal multipliers and credit spreads.
    - In the 2000s-10s the relationship appears to reverse: higher credit spreads associated with lower multipliers.
  - Possible structural changes altering transmission: deeper global financial integration, monetary policy constraints at the zero lower bound, and rising household debt.

- Statistical and identification challenges:
  - Forward-looking nature of credit and term spreads introduces endogeneity concerns complicating identification of causal links between financial frictions and fiscal multipliers.
  - The increased interconnectedness of global financial markets amplifies transmission of financial shocks across borders, complicating attribution in a single-country analysis.

---

### Conclusion (Section 7) — key takeaways and future directions
- Contributions:
  - Introduced government expenditure multipliers that vary across business cycle phases using a TVP-VAR framework, challenging literature assuming stable multiplier–cycle relationships.
  - Documented that average multipliers became significantly smaller since the 1980s, driven by policy shifts (fiscal-monetary mix) rather than recessions per se.
  - Identified a novel transmission puzzle: financial frictions historically amplified multipliers but this relationship reversed in the 21st century, notably during the global financial crisis.

- Suggestions for future research:
  - Use less flexible but more efficient estimators (e.g., approaches similar to Ramey and Zubairy (2018); Bernardini and Peersman (2018)) to validate identified relationships.
  - Expand the fiscal VAR to include additional variables such as public debt and inflation or apply the framework to a broader set of advanced economies.
  - Investigate changing role of financial frictions within a theoretical framework (e.g., Canzoneri et al. (2016)) to explain negative correlation between multipliers and financial frictions during the Dot-com recession and the global financial crisis.
  - Examine evolving fiscal-monetary policy mixes, including unconventional monetary policies (e.g., Bi and Traum (2023)), to assess their influence on fiscal multipliers.

*Source: wpiea2025108-print-pdf - 6.1    Drivers*

### References

### References

### Key methodological points (detrending and estimation)
- Introduces Hamilton (2018)’s detrending procedure to the fiscal multiplier debate:
  - Uses a linear projection model y_{t+h} = B(L) y_t + v_{t+h}, v_{t+h} ∼ i.i.d. N(0, σ^2).
  - For quarterly data Hamilton (2018) recommends h = 8 and a lag polynomial of order 4.
  - Resulting residuals (v̂_{t+h}) represent a stationary zero-mean cyclical component.
- Advantages of Hamilton’s method highlighted:
  - Produces a non-linear trend estimate without specifying functional form of non-linearity.
  - Allows the trend to be influenced by past macroeconomic events (example: pronounced dip after the global financial crisis).
  - Does not produce spurious correlations between cyclical components and other macro series, unlike the Hodrick and Prescott (HP) filter.
  - Produces stationary series in levels, allowing TVP-VAR estimated IRFs to be interpreted as multipliers, not elasticities.
  - Preserves a larger share of low-frequency variation in the target series, avoiding the rescaling bias described in Ramey and Zubairy (2018).
- Comparisons of detrending choices illustrated:
  - Hamilton’s method vs linear trend vs HP filter (λ = 1,600) in Figure 18 (observed US real per capita public expenditure).
  - First differences lack significant low-frequency variation; linear-trend removal can produce non-mean-reverting cyclical components; Hamilton’s method delivers a compromise preserving mean-reversion and low-frequency variation.

### Data preparation, transformations, and samples
- Table 3: Data transformations and sources (exact sample ranges and variable identifiers preserved):
  - R.p.c* GDP: 1948Q1 - 2018Q2; Source: BEA, FRED.
  - R.p.c* public consumption: 1948Q1 - 2018Q2; Source: BEA, FRED.
  - R.p.c* public investment: 1948Q1 - 2018Q2; Source: BEA, FRED.
  - R.p.c* tax receipts: 1948Q1 - 2018Q2; Source: BEA, FRED.
  - R.p.c* net taxes: 1948Q1 - 2018Q2; Source: BEA, FRED.
  - Forecast of public expenditure growth rate: 1966Q4 - 2010Q3; AG12.
  - NBER recessions: 1948Q1 - 2018Q2; USRECQ; Source: FRED.
  - 10-Year to FFR spread: 1962Q1 - 2018Q2; GS10 − DFF; Source: FRED.
  - 5-Year to FFR spread: 1962Q1 - 2018Q2; DGS5 − DFF; Source: FRED.
  - 1-Year to FFR spread: 1962Q1 - 2018Q2; WGS1YR − DFF; Source: FRED.
  - 6-Month to FFR spread: 1962Q1 - 2018Q2; TB6MS − DFF; Source: FRED.
  - 3-Month to FFR spread: 1962Q1 - 2018Q2; TB3MS − DFF; Source: FRED.
- Notation and metadata:
  - * Real per capita terms. TxLy denotes BEA NIPA Table x line y.
  - BEA = Bureau of Economic Analysis; FRED = Federal Reserve Economic Database; AG12 = Auerbach and Gorodnichenko (2012).

### Fiscal VAR, Cholesky factorization, and identification concerns
- Critique of Cholesky decomposition in fiscal VARs where tax revenues are used instead of marginal tax rates:
  - Cholesky imposes a lower-unitriangular contemporaneous structure on [G_t T_t Y_t], assuming innovations in T_t can contemporaneously affect Y_t but not vice versa; this restriction may be unjustified when output can affect tax revenues within the same quarter.
  - In a generic SVAR Y_t = A_0 Y_t + B(L) Y_{t−1} + ε_t, ε_t ∼ N(0, Θ), the reduced form u_t ∼ N(0, Ω) with Ω decomposed as Ω = P′P = C Σ Σ′ C′. The lower unitriangular matrix C contains immediate responses of endogenous variables to structural shocks and relates to A_0 via C = (I_3 − A_0)^{−1}.
  - Example parameterization shown:
    - A_0 = [[0 0 0]; [α_21 0 0]; [α_31 α_32 0]]
    - C = [[1 0 0]; [α_21 1 0]; [α_31 + α_21 α_32 α_32 1]]
  - Immediate output response to a tax shock is given by α_32; this coefficient mixes effects in both directions (output → taxes and taxes → output), preventing clear causal interpretation.
  - Because α_32 also enters the response of output to a government expenditure shock, output responses identified using Cholesky in the Auerbach and Gorodnichenko (2012) setup can be misleading.
- Empirical diagnostic:
  - Figure 20 shows the immediate output response to a tax shock over time obtained using Cholesky decomposition; the immediate response captures the positive effect of output on the tax base, instead of the negative effect of the tax rate on output, indicating incorrect identification.
- Recommendation:
  - Prefer sign restrictions (e.g., Mountford and Uhlig (2009) and Canova and Pappa (2007)) or narrative (IV/Proxy) identification (e.g., Mertens and Ravn (2010); Stock and Watson (2012b); Stock and Watson (2012a); Stock and Watson (2018)) over simple Cholesky in fiscal VARs with tax revenues ordered after government expenditure.

### Identification via mixture of short-term zero and sign restrictions
- The identification strategy implemented (depicted in 3.1) provides an alternative to Blanchard and Perotti (2002):
  - Reduced-form shocks (u_Gt, u_Tt, u_Yt) expressed as linear functions of contemporaneous variables and structural shocks:
    - u_Gt = α_gy t u_Yt + β_gt t ε_Tt + ε_Gt
    - u_Tt = α_ty t u_Yt + β_tg t ε_Gt + ε_Tt
    - u_Yt = α_yg t u_Gt + α_yt t u_Tt + ε_Yt
  - α_gy t and α_ty t capture automatic response of fiscal variables to changes in output (automatic stabilizer effects) and the systematic discretionary response.
  - The focus is on estimating IRFs to random discretionary shocks, specifically ε_Gt (discretionary government expenditure shocks).
  - Solving the system requires imposing a set of assumptions (mixture of short-term zero and sign restrictions) to identify structural shocks.

*Italic source: wpiea2025108-print-pdf - References*

### 1.  Following Blanchard and Perotti (2002) we assumeα

### 1.  Following Blanchard and Perotti (2002) we assumeα

### Assumptions on contemporaneous coefficients and economic channels
- α_gy_t = 0: implies no automatic nor systematic discretionary responses of government expenditure to developments in output.
  - Note: "The absence of a systematic discretionary response is a consequence of the policy implementation lag; the policy-maker will need at least a quarter to come up and execute a discretionary government expenditure package in response to a surprise recession."
- β_gt = 0: restriction inspired by Blanchard and Perotti (2002); authors argued either β_gt or β_tg should be set to zero; since correlation between government expenditure and net taxes is low, both restrictions produced similar results.
- α_ty_t is positive: allows output shocks to affect net taxes through the tax base; positive shock to output expands the tax base and vice versa. Blanchard and Perotti (2002) estimated α_ty_t as a function of two elasticities; average value remained positive.
  - Comment: "Authors acknowledged that they focused on an average value of α_ty_t, while in reality, it should vary over time; our approach allows accounting for that."
- α_yt_t is negative: Blanchard and Perotti (2002) estimated a time-invariant coefficient for deterministic and stochastic trends; both cases produced negative coefficients equal to -0.868 and -0.876, respectively.

### Representation of the system under these assumptions
- Structural shocks expressed as:
  - u_G_t = ε_G_t
  - u_T_t = (α_ty_t α_yg_t + β_tg_t) / (1 − α_ty_t α_yt_t) ε_G_t + 1/(1 − α_ty_t α_yt_t) ε_T_t + α_ty_t/(1 − α_ty_t α_yt_t) ε_Y_t
  - u_Y_t = (α_yt_t β_tg_t + α_yg_t) / (1 − α_ty_t α_yt_t) ε_G_t + α_yt_t/(1 − α_ty_t α_yt_t) ε_T_t + 1/(1 − α_ty_t α_yt_t) ε_Y_t
- Matrix notation:
  - [u_G_t u_T_t u_Y_t]' = [ [c11_t 0 0]; [c21_t c22_t c23_t]; [c31_t c32_t c33_t] ] [ε_G_t ε_T_t ε_Y_t]'
- Sign implications given α_ty positive and α_yt negative:
  - c22 and c33 are both positive time-varying coefficients.
  - c32 is negative and c23 is positive (the authors note only c32 negative is necessary to impose; it implies c23 positive).
  - c11 is positive by definition.
  - Signs of c21 and c31 are not identified by the stated assumptions.

### Identification strategy
- System is underidentified by the above assumptions; solved using a mixture of sign and short-term zero restrictions following Binning (2013).
- Impact matrix restriction Z_t:
  - Z_t = ( ε_G_t ε_T_t ε_Y_t ; G_0 + 0 0 ; T_0 × + × ; Y_0 × − + ) (notation preserved from source)
- Identification allows two-way effects:
  - Output shocks affect tax revenues via the tax base.
  - Tax shocks affect output by changing tax rates.
  - Contemporaneous response of output to a tax shock is restricted to be negative; no sign assumed for contemporaneous response of taxes to output shocks.
  - Empirical approach reportedly delivers contemporaneous effects of opposite signs without imposing the second restriction.

### Model setup (state-space VAR with time-varying parameters and stochastic volatility)
- Main transformed model:
  - Y_t = X_t α + X_t Φ ̃ Ω^(1/2) γ_t + Σ_t u_t, u_t ∼ N(0, I)  (E.1)
  - γ_t = γ_{t−1} + v*_t, v*_t ∼ N(0, I)  (E.2)
  - log(σ_t) = log(σ_{t−1}) + θ_t, θ_t ∼ N(0, W)  (E.3)
  - γ_{j,t} = (β_{j,t} − α_j) / ω_j for j = 1,...,m
- Model decomposition into state-space forms:
  - Model 1:
    - ̃Y_t = W_t γ_t + ε_t
    - γ_t = γ_{t−1} + v*_t  (E.4)
    - where ̃Y_t = Y_t − X_t α and W_t = X_t ̃Ω^(1/2) Φ
    - Model 1 is linear Gaussian; solved using Carter and Kohn (1994).
  - Model 2:
    - ε**_t = 2 × log(σ_t) + log(u_t u'_t)
    - log(σ_t) = log(σ_{t−1}) + θ_t  (E.5)
    - Model 2 is linear but non-Gaussian; solved via Kim et al. (1998) using χ^2_1 distribution approximation by mixture of log-normals.

- Estimation details:
  - Variance-covariance matrix W from state equation sampled from IW( ̄W^−1, ̄T):
    - ̄Q = W + Σ_{t=1}^T θ_t θ'_t
    - ̄T = T + T_α  (expressions preserved as in source)
  - Φ and other elements estimated via linear regression after rearranging E.1 into:
    - Y*_t = Z_t φ + e_t  (E.6)
    - φ contains non-zero off-diagonal elements of Φ
    - Z_t = X_t ̃Ω^(1/2) F_t with F_t defined in block form in the source

- ω sampling and representation:
  - Define stacked matrices Y, X, γ, ε and G_t = X_t diag(γ_t).
  - v_j = g_j ω_j + ε where v_j = Y − X α − G_{\j} ω_{\j}  (E.7)
  - ω_j sampled from conditional posterior: two-component mixture of truncated normals:
    - p(ω_j | Y, α, γ, ω_{\j}, Σ, τ, λ) = ˆπ_j φ_{(−∞,0)}(ω_j | μ_j, τ_j^2) + (1 − ˆπ_j) φ_{(0,∞)}(ω_j | ˆμ_j, ˆτ_j^2)
  - τ^{-2}_j conditional and λ^2 priors sampled as in Belmonte, Koop and Korobolis (2014):
    - (τ^{-2}_j | λ, ω_j) ∼ IG( s, λ^2/2 (ω_j − μ_j)^2 )
    - (λ^2 | τ) ∼ G( λ_01 + m, λ_02 + 1/2 Σ_{j=1}^m τ_j^2 )

### Gibbs sampler steps
- The Gibbs sampler iterates the following draws:
  1. Draw α from p(α | Y_T, γ_T, Σ_T, W, ω, τ, λ, Φ);
  2. Draw γ_T from p(γ_T | Y_T, α, Σ_T, W, ω, τ, λ, Φ);
  3. Draw Σ_T from p(Σ_T | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ);
  4. Draw W from p(W | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ);
  5. Draw ω from p(ω | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ);
  6. Draw τ from p(τ | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ);
  7. Draw λ from p(ω | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ);
  8. Draw Φ from p(Φ | Y_T, α, γ_T, Σ_T, W, ω, τ, λ, Φ).

### Priors specified
- Standard independent priors:
  - α_0 ∼ N(0, I_m)
  - β_0 ∼ N(0, I_m)
  - Σ_0 ∼ N(0, I_n)
- Tobit prior for ω:
  - ω*_j ∼ N(0, τ_j^2)
  - ω_j = 0 if ω*_j ≤ 0; ω_j = ω*_j if ω*_j > 0
- Lasso prior for τ^2_j:
  - τ^2_j ∼ E(λ^2 / 2)
  - λ^2 ∼ G(0.1, 0.1)
- W ∼ IW(n + 11, 0.01^2 ((n + 11 − n − 1) I_n))

*Cyclical Fiscal Multipliers: Policy Mix and Financial Friction Puzzle — Working Paper No. WP/2025/108*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025108-print-pdf.pdf_