## Measuring the Stances of Monetary and Fiscal Policy

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---

### Framework and key definitions
- Model: An empirically plausible extension of the basic New Keynesian model (price indexation, habit persistence, credit constraints, modified intratemporal utility to obtain Okun’s law).
- Monetary policy stance:
  - Measured by the real interest rate gap: given ˆtmpr =, the stance of monetary policy tmp equals the real interest rate gap.
  - Neutral monetary stance measured by the real natural rate of interest; in this framework the real natural rate depends on the stance of fiscal policy.
- Fiscal policy stance:
  - Denoted tfp and measured in monetary policy stance equivalent units; not proportional to the fiscal impulse (the change in the structural primary fiscal balance ratio) under any permissible parameter restrictions in the model.
  - Depends differentially on structural government expenditure and revenue ratios, and is both backward and forward looking (weighted structural primary fiscal balance ratio).
- Automatic fiscal stabilizers:
  - Denoted tfs and enter the Euler equation alongside the real interest rate gap.
- Identification:
  - Use selected approximate linear equilibrium conditions evaluated under perfect foresight, with a predictive discounting parameter µ to uniformly shrink future realizations (µ set to 0.80).

### Estimation approach
- Estimator: Generalized Multivariate Linear Filter (GMLF) — closed form multivariate linear filter that minimizes an objective function trading off cyclical variance and trend smoothness, while imposing quadratic penalties on deviations from G linearly independent dynamic cyclical restrictions and H linearly independent dynamic trend restrictions.
- Observed series (6N = 6 variables): inflation (GDP price deflator), output (real GDP), unemployment rate (civilian), nominal policy interest rate (effective federal funds rate, period average), government expenditure ratio (general government consumption & investment to nominal output), government revenue ratio (output tax rate plus primary fiscal balance ratio to nominal output).
- Sample: 1960Q1 through 2022Q4 (data from Haver Analytics).
- Tuning/calibration choices:
  - Subjective discount factor β set to imply an annualized discount rate of 4.0 percent.
  - Habit persistence α = 0.50.
  - Intertemporal elasticity of substitution σ = 1.00.
  - Credit constrained household share Cϕ = 0.50.
  - Production homogeneity Yϕ set to imply an Okun’s law coefficient of −0.50.
  - Partial indexation γ = 0.50.
  - Nominal rigidity ω set to imply an average reoptimization interval of 4.0 quarters.
  - Steady state output tax rate τ = 0.20.
  - Predictive discounting parameter µ = 0.80.
- Smoothing and weights used in central estimates:
  - For all variables other than output: difference order di = 1 and smoothing parameter 1,i λ = 20.
  - For output: difference order di = 2 and smoothing parameter 2,i λ = 400.
  - Cyclical restriction weights gγ = 1.
  - Trend restriction weight hψ = 0.001.

### Main empirical findings
- Joint estimation matters:
  - Accounting for fiscal policy significantly alters estimated monetary policy stance; abstracting from fiscal policy yields misspecified identifying restrictions and biases.
- Magnitude of differences relative to alternatives:
  - Deviations of the multivariate monetary stance estimate from the estimate that abstracts from fiscal policy are up to 52 basis points (in absolute value).
  - Deviations of the multivariate monetary stance estimate from the corresponding univariate-filter estimate are up to 69 basis points (in absolute value).
- Monetary stance dynamics:
  - The multivariate estimate of the real natural rate of interest is estimated to have fallen more in the aftermath of the Global Financial Crisis when cyclical restrictions account for fiscal policy (reflecting slow output gap recovery and a loose fiscal stance plus automatic stabilizers).
- Fiscal stance dynamics:
  - The multivariate filter based estimate of the stance of fiscal policy fluctuates at business cycle frequencies: generally indicates tightening before recessions and loosening during them.
  - The univariate filter based estimate tracks the trend of the multivariate estimate but shows little variation at business cycle frequencies (less informative).
  - The multivariate-filter estimate of the fiscal impulse fluctuates at business cycle frequencies but is a poor proxy for the stance of fiscal policy; correlation between the multivariate estimates of the stance of fiscal policy and the fiscal impulse is 0.21.
- Intertemporal correlation patterns (from multivariate estimates):
  - Monetary stance: positively correlated with contemporaneous and lagged inflation and output gaps; negatively correlated with leads of these gaps — consistent with cyclical inflation/output stabilization objectives.
  - Fiscal stance: approximately uncorrelated with the inflation gap at all horizons; positively correlated with the output gap at all horizons — reflecting countercyclical stabilization and high inertia (positive correlation with leads of the output gap), making fiscal policy unsuitable for fine-tuning.

### Robustness and sensitivity
- The GMLF depends on many tuning and structural parameters; sensitivity analysis is straightforward and reported.
- Sensitivity to smoothing parameters (Table 1): root mean squared deviations (percentage points) from central estimates show:
  - Monetary stance tmp sensitive to smoothness of trend inflation and the nominal natural rate of interest.
  - Fiscal stance tfp sensitive to smoothness of potential output, structural government expenditure ratio, and structural government revenue ratio.
  - Representative entries (root mean squared deviations) reported across selected λ perturbations (excerpt):
    - tmp: 0.342, 0.420, 0.099, 0.177, 0.004, 0.007, 0.798, 0.811, 0.094, 0.141, 0.050, 0.064.
    - tfp: 0.012, 0.020, 1.354, 2.203, 0.054, 0.089, 0.049, 0.061, 2.464, 1.653, 1.041, 0.479.
- Sensitivity to weight parameters (Table 2): root mean squared deviations (percentage points) from central estimates show:
  - Monetary stance tmp varies with the degree to which the Phillips curve and Euler equation are conditioned on (examples: tmp = 0.242, 0.233, 0.205, 0.132, 0.008, 0.007, 0.007, 0.021).
  - Fiscal stance tfp varies strongly with the degree to which the Euler equation is conditioned on (examples: tfp = 0.008, 0.007, 3.982, 2.916, 0.101, 0.089, 0.002, 0.007).
- Sensitivity to structural parameter perturbations (Table 3): root mean squared deviations (percentage points) from central estimates show:
  - Many structural parameter changes affect at least one stance estimate; parameters entering the Euler equation and trend relationships are especially influential.
  - Representative entries for tfp (percentage points): 0.000, 0.000, 1.983, 5.982, 5.966, 1.996, 3.716, 14.138, 0.066, 0.095, 0.000, 0.000, 0.011, 0.001, 0.885, 1.174, 5.426, 5.616.
  - Representative entries for tmp (percentage points): 0.001, 0.001, 0.137, 0.115, 0.104, 0.103, 0.084, 0.097, 0.013, 0.010, 0.007, 0.004, 0.145, 0.018, 0.020, 0.021, 0.254, 0.250.
- Interpretation: sensitivity analysis highlights the central importance of the Euler equation and the output gap in jointly estimating monetary and fiscal stances.

### Conclusions and policy implications
- Joint estimation required:
  - Measures of the stances of monetary and fiscal policy are closely interrelated; estimating them jointly avoids biases from misspecified restrictions that abstract from fiscal policy.
- Monetary vs fiscal objectives and summarizability:
  - Monetary policy: inflation and output stabilization objectives are cyclical and mutually reinforcing; the stance of monetary policy can be summarized with a single measure (real interest rate gap).
  - Fiscal policy: countercyclical stabilization and debt sustainability objectives operate at different frequencies and can conflict; the stance of fiscal policy is not amenable to a single aggregate summary without abstracting from one objective.
- Practical implication:
  - The fiscal impulse (change in structural primary fiscal balance ratio) is a poor proxy for the stance of fiscal policy; fiscal stance measures should account for differential expenditure vs revenue effects and forward-looking dynamics.
- Caveat:
  - The focus on the countercyclical stabilization objective for fiscal stance measurement assumes adequate fiscal space to abstract from debt sustainability; for some economies/times this assumption is violated, limiting applicability.

*Source — IMF Working Paper chapter "Measuring the Stances of Monetary and Fiscal Policy" (content unit: wpiea2023106-print-pdf - References).*

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

### Measuring the Stances of Monetary and Fiscal Policy

### Framework and key definitions
- Model: An empirically plausible extension of the basic New Keynesian model (price indexation, habit persistence, credit constraints, modified intratemporal utility to obtain Okun’s law).
- Monetary policy stance:
  - Measured by the real interest rate gap: given ˆtmpr =, the stance of monetary policy tmp equals the real interest rate gap.
  - Neutral monetary stance measured by the real natural rate of interest; in this framework the real natural rate depends on the stance of fiscal policy.
- Fiscal policy stance:
  - Denoted tfp and measured in monetary policy stance equivalent units; not proportional to the fiscal impulse (the change in the structural primary fiscal balance ratio) under any permissible parameter restrictions in the model.
  - Depends differentially on structural government expenditure and revenue ratios, and is both backward and forward looking (weighted structural primary fiscal balance ratio).
- Automatic fiscal stabilizers:
  - Denoted tfs and enter the Euler equation alongside the real interest rate gap.
- Identification: use selected approximate linear equilibrium conditions evaluated under perfect foresight, with a predictive discounting parameter µ to uniformly shrink future realizations (µ set to 0.80).

### Estimation approach
- Estimator: Generalized Multivariate Linear Filter (GMLF) — closed form multivariate linear filter that minimizes an objective function trading off cyclical variance and trend smoothness, while imposing quadratic penalties on deviations from G linearly independent dynamic cyclical restrictions and H linearly independent dynamic trend restrictions.
- Observed series (6N = 6 variables): inflation (GDP price deflator), output (real GDP), unemployment rate (civilian), nominal policy interest rate (effective federal funds rate, period average), government expenditure ratio (general government consumption & investment to nominal output), government revenue ratio (output tax rate plus primary fiscal balance ratio to nominal output).
- Sample: 1960Q1 through 2022Q4 (data from Haver Analytics).
- Tuning/calibration choices highlighted:
  - Subjective discount factor β set to imply an annualized discount rate of 4.0 percent.
  - Habit persistence α = 0.50.
  - Intertemporal elasticity of substitution σ = 1.00.
  - Credit constrained household share Cϕ = 0.50.
  - Production homogeneity Yϕ set to imply an Okun’s law coefficient of −0.50.
  - Partial indexation γ = 0.50.
  - Nominal rigidity ω set to imply an average reoptimization interval of 4.0 quarters.
  - Steady state output tax rate τ = 0.20.
  - Predictive discounting parameter µ = 0.80.
- Smoothing and weights used in central estimates:
  - For all variables other than output: difference order di = 1 and smoothing parameter 1,i λ = 20.
  - For output: difference order di = 2 and smoothing parameter 2,i λ = 400.
  - Cyclical restriction weights gγ = 1.
  - Trend restriction weight hψ = 0.001.

### Main empirical findings
- Joint estimation matters:
  - Accounting for fiscal policy significantly alters estimated monetary policy stance; abstracting from fiscal policy yields misspecified identifying restrictions and biases.
- Magnitude of differences relative to alternatives:
  - Deviations of the multivariate monetary stance estimate from the estimate that abstracts from fiscal policy are up to 52 basis points (in absolute value).
  - Deviations of the multivariate monetary stance estimate from the corresponding univariate-filter estimate are up to 69 basis points (in absolute value).
- Monetary stance dynamics:
  - The multivariate estimate of the real natural rate of interest is estimated to have fallen more in the aftermath of the Global Financial Crisis when cyclical restrictions account for fiscal policy (reflecting slow output gap recovery and a loose fiscal stance plus automatic stabilizers).
- Fiscal stance dynamics:
  - The multivariate filter based estimate of the stance of fiscal policy fluctuates at business cycle frequencies: generally indicates tightening before recessions and loosening during them.
  - The univariate filter based estimate tracks the trend of the multivariate estimate but shows little variation at business cycle frequencies (less informative).
  - The multivariate-filter estimate of the fiscal impulse fluctuates at business cycle frequencies but is a poor proxy for the stance of fiscal policy; correlation between the multivariate estimates of the stance of fiscal policy and the fiscal impulse is 0.21.
- Intertemporal correlation patterns (from multivariate estimates):
  - Monetary stance: positively correlated with contemporaneous and lagged inflation and output gaps; negatively correlated with leads of these gaps — consistent with cyclical inflation/output stabilization objectives.
  - Fiscal stance: approximately uncorrelated with the inflation gap at all horizons; positively correlated with the output gap at all horizons — reflecting countercyclical stabilization and high inertia (positive correlation with leads of the output gap), making fiscal policy unsuitable for fine-tuning.

### Robustness and sensitivity
- The GMLF depends on many tuning and structural parameters; sensitivity analysis is straightforward and reported.
- Sensitivity to smoothing parameters (Table 1): root mean squared deviations (percentage points) from central estimates show:
  - Monetary stance tmp sensitive to smoothness of trend inflation and the nominal natural rate of interest.
  - Fiscal stance tfp sensitive to smoothness of potential output, structural government expenditure ratio, and structural government revenue ratio.
  - Representative entries (root mean squared deviations) reported across selected λ perturbations (excerpt):
    - tmp: 0.342, 0.420, 0.099, 0.177, 0.004, 0.007, 0.798, 0.811, 0.094, 0.141, 0.050, 0.064.
    - tfp: 0.012, 0.020, 1.354, 2.203, 0.054, 0.089, 0.049, 0.061, 2.464, 1.653, 1.041, 0.479.
- Sensitivity to weight parameters (Table 2): root mean squared deviations (percentage points) from central estimates show:
  - Monetary stance tmp varies with the degree to which the Phillips curve and Euler equation are conditioned on (examples: tmp = 0.242, 0.233, 0.205, 0.132, 0.008, 0.007, 0.007, 0.021).
  - Fiscal stance tfp varies strongly with the degree to which the Euler equation is conditioned on (examples: tfp = 0.008, 0.007, 3.982, 2.916, 0.101, 0.089, 0.002, 0.007).
- Sensitivity to structural parameter perturbations (Table 3): root mean squared deviations (percentage points) from central estimates show:
  - Many structural parameter changes affect at least one stance estimate; parameters entering the Euler equation and trend relationships are especially influential.
  - Representative entries for tfp (percentage points): 0.000, 0.000, 1.983, 5.982, 5.966, 1.996, 3.716, 14.138, 0.066, 0.095, 0.000, 0.000, 0.011, 0.001, 0.885, 1.174, 5.426, 5.616.
  - Representative entries for tmp (percentage points): 0.001, 0.001, 0.137, 0.115, 0.104, 0.103, 0.084, 0.097, 0.013, 0.010, 0.007, 0.004, 0.145, 0.018, 0.020, 0.021, 0.254, 0.250.
- Interpretation: sensitivity analysis highlights the central importance of the Euler equation and the output gap in jointly estimating monetary and fiscal stances.

### Conclusions and policy implications
- Joint estimation required: measures of the stances of monetary and fiscal policy are closely interrelated; estimating them jointly avoids biases from misspecified restrictions that abstract from fiscal policy.
- Monetary vs fiscal objectives and summarizability:
  - Monetary policy: inflation and output stabilization objectives are cyclical and mutually reinforcing; the stance of monetary policy can be summarized with a single measure (real interest rate gap).
  - Fiscal policy: countercyclical stabilization and debt sustainability objectives operate at different frequencies and can conflict; the stance of fiscal policy is not amenable to a single aggregate summary without abstracting from one objective.
- Practical implication: the fiscal impulse (change in structural primary fiscal balance ratio) is a poor proxy for the stance of fiscal policy; fiscal stance measures should account for differential expenditure vs revenue effects and forward-looking dynamics.
- Caveat: the focus on the countercyclical stabilization objective for fiscal stance measurement assumes adequate fiscal space to abstract from debt sustainability; for some economies/times this assumption is violated, limiting applicability.

*Italic: Source — IMF Working Paper chapter "Measuring the Stances of Monetary and Fiscal Policy" (content unit: wpiea2023106-print-pdf - References).*

### REFERENCES

### REFERENCES

### Core empirical and theoretical frameworks
- Calvo, G. (1983), “Staggered Prices in a Utility-Maximizing Framework”, Journal of Monetary Economics, Vol. 12, pp. 383-398.
- Lucas, R. (1980), “Two Illustrations of the Quantity Theory of Money”, American Economic Review, Vol. 70, pp. 1005-1014.
- Woodford, M. (2003), Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press.
- Galí, J. (2015), Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework and Its Applications, Princeton University Press.
- Romer, D. (2019), Advanced Macroeconomics, McGraw-Hill.

### New Keynesian, behavioral, and DSGE contributions
- Gabaix, X. (2020), “A Behavioral New Keynesian Model”, American Economic Review, Vol. 110, pp. 2271-2327.
- Smets, F. and R. Wouters (2003), “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area”, Journal of the European Economic Association, Vol. 1, pp. 1123-1175.
- Galí, J., D. López-Salido and J. Vallés (2007), “Understanding the Effects of Government Spending on Consumption”, Journal of the European Economic Association, Vol. 5, pp. 227-270.

### Monetary and fiscal stance measurement and policy analysis
- Batini, N., A. Cantelmo, G. Melina and S. Villa (2021), “How Loose, How Tight? A Measure of Monetary and Fiscal Stance for the Euro Area”, Oxford Economic Papers, Vol. 73, pp. 1536-1556.
- Polito, V. and M. Wickens (2012), “A Model-Based Indicator of the Fiscal Stance”, European Economic Review, Vol. 56, pp. 526-551.
- Whalen, C. and F. Reichling (2015), “The Fiscal Multiplier and Economic Policy Analysis in the United States”, Contemporary Economic Policy, Vol. 33, pp. 735-746.

### Time series methods, filtering, and estimation techniques
- Clark, P. (1989), “Trend Reversion in Real Output and Unemployment”, Journal of Econometrics, Vol. 40, pp. 15-32.
- Hodrick, R. and E. Prescott (1997), “Post-War U.S. Business Cycles: A Descriptive Empirical Investigation”, Journal of Money, Credit and Banking, Vol. 29, pp. 1-16.
- Kalman, R. (1960), “A New Approach to Linear Filtering and Prediction Problems”, Transactions ASME Journal of Basic Engineering, Vol. 82, pp. 35-45.
- Laubach, T. and J. Williams (2003), “Measuring the Natural Rate of Interest”, Review of Economics and Statistics, Vol. 85, pp. 1063-1070.
- Vitek, F. (2018), “A Closed Form Multivariate Linear Filter”, IMF Working Paper, 275.

*Measuring the Stances of Monetary and Fiscal Policy  
Working Paper No. WP/2023/106*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023106-print-pdf.pdf_