## _wp10149

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---

### I. Introduction
- Challenge: Estimating potential output and output gap in transition economies is difficult due to data scarcity, time-varying natural unemployment, and end-point bias of atheoretical filters (HP).
- Approach: Model-based multivariate filter (two-equation AD-AS system) with Bayesian estimation to combine data and priors derived from previous studies and economic theory.
- Core model features:
  - Output gap evolves as a function of lagged output gap, real interest rate (RR), and real exchange rate (z), augmented by HP-measure of trading partners’ output gap (Wygap).
  - Phillips-curve-type inflation equation links core inflation to output gap, exchange rate depreciation, and supply-shock variables (e.g., raw food price changes).
  - Potential output follows a random walk in logs with a time-varying slope μ.
- Motivation for Bayesian methods:
  - Short quarterly series for Vietnam make classical estimation unreliable.
  - Bayesian priors improve identification and interpretability in short samples.

### II. Growth and inflation developments (Vietnam)
- Historical trajectory:
  - Hyperinflation above 300 percent in 1986-88; brought down below 20 percent by 1992 and close to 10 percent in 1995.
  - Mild deflation in 2000-01; subdued inflation in 2002-03.
  - Strong growth and rising inflation 2004–2007 driven by consumption and exports and international commodity prices.
  - Growth slowed to 6¼ percent in 2008 (slowest since 1999); inflation peaked mid-2008 then moderated.
- Empirical observations:
  - GDP growth correlated with trading partners’ growth and the real interest rate; weaker visible relationship with real effective exchange rate.
  - Core inflation appears led by output growth and strongly affected by supply shocks (relative raw food price changes).

### III. Model and estimation procedure
- Model specification:
  - Output gap: ygap_t = 100 × [log(Y_t) − log(Y*_t)]; dynamic equation includes lagged ygap, deviations of RR and z from equilibrium, and Wygap.
  - Phillips curve: core inflation π_c,t (annualized quarterly change) depends on lagged inflation, lagged output gap, changes in real exchange rate, relative raw food price change (rpfood_t), and the lagged gap between headline and core inflation.
  - Potential output: log(Y*_t) evolves with stochastic slope μ_t following random walk specifications (equations (3) and (4)).
- Key model properties:
  - HP filter with smoothing parameter 1600 is a special case of the potential-output specification when specific variances are set: *22, ygapu, Yuu, uμσβ  = 0,1600,0 and ygapα = 0.
- Data:
  - Quarterly sample: 1999 Q2 to 2008 Q4.
  - Sources: State Bank of Vietnam (prime lending rate), General Statistical Office of Vietnam (GDP, CPI, core CPI, raw food prices), IMF WEO (real effective exchange rate, GDP in trading partners).
  - Real interest rate: calculated using core CPI.
  - Seasonally adjusted with X12 except log(GDP) (seasonal adjustment via auxiliary state-space model).
- Bayesian estimation:
  - Priors: Normal for coefficients (means based on literature; standard deviations equal to means for baseline), inverse gamma for variance parameters with c set to 4.01.
  - Restrictions on priors: 0 < β_lag < 1, β_RR < 0, β_z > 0; 0 < α_ygap < 1, 0 < α_lagπ < 1, α_z > 0, α_f > 0, α_ecm > 0.
  - MCMC algorithm: burn-in of 10000 draws; remaining 100000 draws used for inference. Sampling steps include simulation smoother (de Jong and Shephard 1995) and conditional draws for variance and equation coefficients; draws rejected if coefficient sign/inequality restrictions violated.
  - Seasonal adjustment: state-space seasonal model allowing time-varying seasonality; when ω_σ^2 = 0 seasonal effects sum to zero; when ω_σ^2 > 0 seasonal sum is white noise.

### IV. Results
- Posterior coefficients — output-gap equation:
  - Interest-rate coefficient: small and negative; indicates a weak short-term monetary transmission on output gap. Robust to alternative equilibrium measures.
  - Exchange-rate coefficient: much lower than literature prior; suggests weak impact of real exchange rate deviations on output (attributed to large share of primary commodities in exports).
  - Trading-partners’ output gap coefficient (Wygap): close to prior and estimated relatively precisely (consistent with high openness).
  - Lagged output gap coefficient: slightly lower than prior but within literature range.
- Posterior coefficients — Phillips curve:
  - Lagged inflation coefficient: high (inflation inertia), though lower than prior.
  - Output-gap coefficient: higher than prior, implying inflation provides substantial information on output gap.
  - Relative raw food-price coefficient (fα): high and precisely estimated—supply shocks strongly affect core inflation.
  - Exchange-rate coefficient in Phillips curve: close to prior.
  - Short-term second-round effects (ecmα): relatively weak.
- Posterior variances (selected):
  - Posterior mean of output gap shock variance 2_ygap_u_σ is smaller than prior.
  - Posterior mean of potential-output slope shock variance 2_u_μ_σ is close to prior.
  - Ratio 2_u_μ_σ / 2_ygap_u_σ is lower than the HP-restriction of 1600.
  - Posterior mean of permanent shock variance *2_Y_u_σ is also lower than prior.
  - Inverse signal-to-noise ratio (*22/ygapYuuσσ) close to prior.
- Key numeric parameter estimates (Prior mean / Posterior mean / Posterior Std. Dev. / Posterior 5th and 95th percentiles where available):
  - Variances on innovations:
    - 2_ygap_u_σ: Prior mean 0.166; Posterior mean 0.0224; Posterior Std. Dev. 0.0364; 5th percentile 0.0107; 95th percentile 0.0563.
    - *2_Y_u_σ: Prior mean 0.166; Posterior mean 0.0306; Posterior Std. Dev. 0.0561; 5th percentile 0.0153; 95th percentile 0.0790.
    - 2_u_μ_σ: Prior mean 0.0001; Posterior mean 0.0001; Posterior Std. Dev. 0.0001; 5th percentile 0.0000; 95th percentile 0.0003.
    - 2_u_π_σ: Prior mean 28.179; Posterior mean 5.9458; Posterior Std. Dev. 8.5793; 5th percentile 1.9348; 95th percentile 12.1437.
  - Output-gap equation coefficients:
    - lag β: Prior 0.700 / Posterior mean 0.6562 / Std. Dev. 0.1568 / 5th 0.2211 / 95th 0.8646.
    - RRgap β: Prior -0.100 / Posterior mean -0.0730 / Std. Dev. 0.0320 / 5th -0.1285 / 95th -0.0224.
    - zgap β: Prior 0.050 / Posterior mean 0.0104 / Std. Dev. 0.0083 / 5th 0.0007 / 95th 0.0264.
    - Wygap β: Prior 0.250 / Posterior mean 0.2211 / Std. Dev. 0.0848 / 5th 0.0849 / 95th 0.3635.
  - Phillips curve coefficients:
    - ygap α: Prior 0.300 / Posterior mean 0.4041 / Std. Dev. 0.2325 / 5th 0.0605 / 95th 0.8189.
    - lag π α: Prior 0.900 / Posterior mean 0.7375 / Std. Dev. 0.1225 / 5th 0.5263 / 95th 0.9324.
    - z α: Prior 0.200 / Posterior mean 0.2059 / Std. Dev. 0.1181 / 5th 0.0311 / 95th 0.4162.
    - f α (relative food price): Prior 0.200 / Posterior mean 0.2172 / Std. Dev. 0.0432 / 5th 0.1459 / 95th 0.2884.
    - ecm α: Prior 0.100 / Posterior mean 0.0754 / Std. Dev. 0.0925 / 5th -0.0767 / 95th 0.2280.
- Estimated output gap series:
  - Below-potential activity: late-1999 to 2005.
  - Overheating: 2006–2008 (positively and significantly different from zero).
  - Turnaround: late 2008 into negative cyclical position.
  - Uncertainty: considerable near end-sample; posterior distribution skewed with mode closer to zero than mean in mid-sample.
- Comparison with HP filter:
  - Model-based series differs materially from HP: wider negative gap in 2001-04; HP peaks mid-2007 then falls negative at end-sample, while model peaks 2008Q1 and remains positive through 2008.
  - Both HP and model-based estimates suffer from end-point revision problems, but model revisions reflect parameter re-estimation and can be reduced with stronger priors.
- Robustness to revisions:
  - Short-sample HP underestimates excess demand at end-2007 compared to full sample.
  - Model-based estimates under partial data underestimate output gap throughout sample.
  - Tighter priors (mean-to-std-dev ratio set to 5 vs. 1 baseline) yield similar full-sample estimate with substantially fewer revisions over time.

### V. Conclusions
- Methodological contribution:
  - Bayesian estimation of a two-equation AD-AS model provides a meaningful output gap measure for Vietnam despite short and imperfect data.
  - Priors based on literature and country specifics help identification and reduce implausible behavior in small samples.
- Empirical conclusions for Vietnam:
  - Coefficients align with economic theory: weak short-term interest-rate and exchange-rate channels, strong openness effect, high inflation inertia, large supply-shock influence (food prices), and a sizable output-gap effect on inflation.
  - Model-based output gap indicates extended below-potential period in early 2000s, overheating in 2006–08, and a cyclical downturn in late 2008.
- Practical trade-offs:
  - Stronger priors reduce revisions but dampen information extraction from data; desirable when data are short or poor.
  - The model, even with strong priors, is better grounded in economic theory than the atheoretical HP filter.

### Appendix (methods and implementation)
- State-space representation:
  - System cast into state-space form where states include lagged output gap, potential output log(Y*), and slope μ_t; measurement variables are log(GDP) and inflation.
  - Matrices T, Z, H, G, d_t, c_t contain hyper-parameters linking observed signals to states.
- Bayesian estimation details:
  - Priors for variance parameters: inverse gamma with c = 4.01 and scale S_σ set to 2c− times appropriate scale variables (variance of HP output-gap for *2 and ygapYuuσσ; 1/1600 of this variance for 2_u_μ_σ; variance of inflation for 2_u_π_σ).
  - Baseline priors for output-gap and Phillips-curve coefficients: normal with mean equal to literature-based values and standard deviation equal to means.
  - MCMC algorithm:
    - Initialize φ (hyper-parameters).
    - Sample states α and errors u using simulation smoother.
    - Draw variance parameters from conditional inverse-gamma posteriors.
    - Draw output-gap coefficients (conditional normal) and accept if sign/inequality restrictions met; otherwise reject and resample.
    - Draw Phillips-curve coefficients similarly with restrictions.
    - Burn-in: 10000 draws. Retained draws: 100000 for inference. Multiple starting points used to verify convergence.
- Seasonal adjustment of GDP:
  - Auxiliary state-space seasonal model decomposes y_t into trend μ_t, seasonal γ_t, and irregular ξ_t.
  - Trend: random walk with stochastic slope; seasonal evolution allows time variation via ω_σ^2 parameter.
  - State-space seasonal adjustment addresses X12 shortcomings (time-varying seasonal pattern), producing cleaner first differences of log GDP.

*Source: Staff estimates and analysis from the document._wp10149 - References .............................................................................................................*

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

### _wp10149 - References .............................................................................................................

### I. Introduction
- Challenge: Estimating potential output and output gap in transition economies is difficult due to data scarcity, time-varying natural unemployment, and end-point bias of atheoretical filters (HP).
- Approach: Use a model-based multivariate filter (two-equation AD-AS system) with Bayesian estimation to combine data and priors derived from previous studies and economic theory.
- Core model features:
  - Output gap evolves as a function of lagged output gap, real interest rate (RR), and real exchange rate (z), augmented by HP-measure of trading partners’ output gap (Wygap).
  - Phillips-curve-type inflation equation links core inflation to output gap, exchange rate depreciation, and supply-shock variables (e.g., raw food price changes).
  - Potential output follows a random walk in logs with a time-varying slope μ.
- Motivation for Bayesian methods:
  - Short quarterly series for Vietnam make classical estimation unreliable.
  - Bayesian priors improve identification and interpretability in short samples.

### II. Growth and inflation developments (Vietnam)
- Historical trajectory:
  - Hyperinflation above 300 percent in 1986-88; brought down below 20 percent by 1992 and close to 10 percent in 1995.
  - Mild deflation in 2000-01; subdued inflation in 2002-03.
  - Strong growth and rising inflation 2004–2007 driven by consumption and exports and international commodity prices.
  - Growth slowed to 6¼ percent in 2008 (slowest since 1999); inflation peaked mid-2008 then moderated.
- Empirical observations (Figure 1 synopsis):
  - GDP growth correlated with trading partners’ growth and the real interest rate; weaker visible relationship with real effective exchange rate.
  - Core inflation appears led by output growth and strongly affected by supply shocks (relative raw food price changes).

### III. Model and estimation procedure
- Model specification (equations summarized):
  - Output gap: ygap_t = 100 × [log(Y_t) − log(Y*_t)]; dynamic equation includes lagged ygap, deviations of RR and z from equilibrium, and Wygap.
  - Phillips curve: core inflation π_c,t (annualized quarterly change) depends on lagged inflation, lagged output gap, changes in real exchange rate, relative raw food price change (rpfood_t), and the lagged gap between headline and core inflation.
  - Potential output: log(Y*_t) evolves with stochastic slope μ_t following random walk specifications (equations (3) and (4)).
- Key model properties:
  - HP filter with smoothing parameter 1600 is a special case of the potential-output specification when specific variances are set: *22, ygapu, Yuu, uμσβ  = 0,1600,0 and ygapα = 0.
- Data:
  - Quarterly sample: 1999 Q2 to 2008 Q4.
  - Sources: State Bank of Vietnam (prime lending rate), General Statistical Office of Vietnam (GDP, CPI, core CPI, raw food prices), IMF WEO (real effective exchange rate, GDP in trading partners).
  - Real interest rate: calculated using core CPI.
  - Seasonally adjusted with X12 except log(GDP) (seasonal adjustment via auxiliary state-space model).
- Bayesian estimation:
  - Priors: Normal for coefficients (means based on literature; standard deviations equal to means for baseline), inverse gamma for variance parameters with c set to 4.01.
  - Restrictions on priors: 0 < β_lag < 1, β_RR < 0, β_z > 0; 0 < α_ygap < 1, 0 < α_lagπ < 1, α_z > 0, α_f > 0, α_ecm > 0.
  - MCMC algorithm: burn-in of 10000 draws; remaining 100000 draws used for inference. Sampling steps include simulation smoother (de Jong and Shephard 1995) and conditional draws for variance and equation coefficients; draws rejected if coefficient sign/inequality restrictions violated.
  - Seasonal adjustment: state-space seasonal model allowing time-varying seasonality; when ω_σ^2 = 0 seasonal effects sum to zero; when ω_σ^2 > 0 seasonal sum is white noise.

### IV. Results
- Posterior coefficients (summary findings):
  - Output-gap equation:
    - Interest-rate coefficient: small and negative; indicates a weak short-term monetary transmission on output gap. Robust to alternative equilibrium measures.
    - Exchange-rate coefficient: much lower than literature prior; suggests weak impact of real exchange rate deviations on output (attributed to large share of primary commodities in exports).
    - Trading-partners’ output gap coefficient (Wygap): close to prior and estimated relatively precisely (consistent with high openness).
    - Lagged output gap coefficient: slightly lower than prior but within literature range.
  - Phillips curve:
    - Lagged inflation coefficient: high (inflation inertia), though lower than prior.
    - Output-gap coefficient: higher than prior, implying inflation provides substantial information on output gap.
    - Relative raw food-price coefficient (fα): high and precisely estimated—supply shocks strongly affect core inflation.
    - Exchange-rate coefficient in Phillips curve: close to prior.
    - Short-term second-round effects (ecmα): relatively weak.
- Posterior variances:
  - Posterior mean of output gap shock variance 2_ygap_u_σ is smaller than prior.
  - Posterior mean of potential-output slope shock variance 2_u_μ_σ is close to prior.
  - Ratio 2_u_μ_σ / 2_ygap_u_σ is lower than the HP-restriction of 1600 (Figure 2).
  - Posterior mean of permanent shock variance *2_Y_u_σ is also lower than prior.
  - Inverse signal-to-noise ratio (*22/ygapYuuσσ) close to prior.
- Key numeric parameter estimates (Table 1 — Priors and Posteriors; listed as Prior mean / Posterior mean / Posterior Std. Dev. / Posterior 5th and 95th percentiles where available):
  - Variances on innovations:
    - 2_ygap_u_σ: Prior mean 0.166; Posterior mean 0.0224; Posterior Std. Dev. 0.0364; 5th percentile 0.0107; 95th percentile 0.0563.
    - *2_Y_u_σ: Prior mean 0.166; Posterior mean 0.0306; Posterior Std. Dev. 0.0561; 5th percentile 0.0153; 95th percentile 0.0790.
    - 2_u_μ_σ: Prior mean 0.0001; Posterior mean 0.0001; Posterior Std. Dev. 0.0001; 5th percentile 0.0000; 95th percentile 0.0003.
    - 2_u_π_σ: Prior mean 28.179; Posterior mean 5.9458; Posterior Std. Dev. 8.5793; 5th percentile 1.9348; 95th percentile 12.1437.
  - Output-gap equation coefficients (prior mean / posterior mean / posterior Std. Dev. / posterior 5th & 95th percentiles):
    - lag β: Prior 0.700 / Posterior mean 0.6562 / Std. Dev. 0.1568 / 5th 0.2211 / 95th 0.8646.
    - RRgap β: Prior -0.100 / Posterior mean -0.0730 / Std. Dev. 0.0320 / 5th -0.1285 / 95th -0.0224.
    - zgap β: Prior 0.050 / Posterior mean 0.0104 / Std. Dev. 0.0083 / 5th 0.0007 / 95th 0.0264.
    - Wygap β: Prior 0.250 / Posterior mean 0.2211 / Std. Dev. 0.0848 / 5th 0.0849 / 95th 0.3635.
  - Phillips curve coefficients:
    - ygap α: Prior 0.300 / Posterior mean 0.4041 / Std. Dev. 0.2325 / 5th 0.0605 / 95th 0.8189.
    - lag π α: Prior 0.900 / Posterior mean 0.7375 / Std. Dev. 0.1225 / 5th 0.5263 / 95th 0.9324.
    - z α: Prior 0.200 / Posterior mean 0.2059 / Std. Dev. 0.1181 / 5th 0.0311 / 95th 0.4162.
    - f α (relative food price): Prior 0.200 / Posterior mean 0.2172 / Std. Dev. 0.0432 / 5th 0.1459 / 95th 0.2884.
    - ecm α: Prior 0.100 / Posterior mean 0.0754 / Std. Dev. 0.0925 / 5th -0.0767 / 95th 0.2280.
- Estimated output gap series (Figure 3 summary):
  - Below-potential activity: late-1999 to 2005.
  - Overheating: 2006–2008 (positively and significantly different from zero).
  - Turnaround: late 2008 into negative cyclical position.
  - Uncertainty: considerable near end-sample; posterior distribution skewed with mode closer to zero than mean in mid-sample.
- Comparison with HP filter:
  - Model-based series differs materially from HP: wider negative gap in 2001-04; HP peaks mid-2007 then falls negative at end-sample, while model peaks 2008Q1 and remains positive through 2008.
  - Both HP and model-based estimates suffer from end-point revision problems, but model revisions reflect parameter re-estimation and can be reduced with stronger priors.
- Robustness to revisions:
  - Short-sample HP underestimates excess demand at end-2007 compared to full sample.
  - Model-based estimates under partial data underestimate output gap throughout sample.
  - Tighter priors (mean-to-std-dev ratio set to 5 vs. 1 baseline) yield similar full-sample estimate with substantially fewer revisions over time.

### V. Conclusions
- Methodological contribution:
  - Bayesian estimation of a two-equation AD-AS model provides a meaningful output gap measure for Vietnam despite short and imperfect data.
  - Priors based on literature and country specifics help identification and reduce implausible behavior in small samples.
- Empirical conclusions for Vietnam:
  - Coefficients align with economic theory: weak short-term interest-rate and exchange-rate channels, strong openness effect, high inflation inertia, large supply-shock influence (food prices), and a sizable output-gap effect on inflation.
  - Model-based output gap indicates extended below-potential period in early 2000s, overheating in 2006–08, and a cyclical downturn in late 2008.
- Practical trade-offs:
  - Stronger priors reduce revisions but dampen information extraction from data; desirable when data are short or poor.
  - The model, even with strong priors, is better grounded in economic theory than the atheoretical HP filter.

### Appendix (methods and implementation)
- State-space representation:
  - System cast into state-space form where states include lagged output gap, potential output log(Y*), and slope μ_t; measurement variables are log(GDP) and inflation.
  - Matrices T, Z, H, G, d_t, c_t contain hyper-parameters linking observed signals to states.
- Bayesian estimation details:
  - Priors for variance parameters: inverse gamma with c = 4.01 and scale S_σ set to 2c− times appropriate scale variables (variance of HP output-gap for *2 and ygapYuuσσ; 1/1600 of this variance for 2_u_μ_σ; variance of inflation for 2_u_π_σ).
  - Baseline priors for output-gap and Phillips-curve coefficients: normal with mean equal to literature-based values and standard deviation equal to means.
  - MCMC algorithm:
    - Initialize φ (hyper-parameters).
    - Sample states α and errors u using simulation smoother.
    - Draw variance parameters from conditional inverse-gamma posteriors.
    - Draw output-gap coefficients (conditional normal) and accept if sign/inequality restrictions met; otherwise reject and resample.
    - Draw Phillips-curve coefficients similarly with restrictions.
    - Burn-in: 10000 draws. Retained draws: 100000 for inference. Multiple starting points used to verify convergence.
- Seasonal adjustment of GDP:
  - Auxiliary state-space seasonal model decomposes y_t into trend μ_t, seasonal γ_t, and irregular ξ_t.
  - Trend: random walk with stochastic slope; seasonal evolution allows time variation via ω_σ^2 parameter.
  - State-space seasonal adjustment addresses X12 shortcomings (time-varying seasonal pattern), producing cleaner first differences of log GDP (Figure 6).

*Source: Staff estimates and analysis from the document._wp10149 - References .............................................................................................................*

### REFERENCES

### _wp10149 - REFERENCES

### References

- Aiyar, Shekhar & Ivan Tchakarov, 2008. "Much Ado About Nothing? Estimating the Impact of a U.S. Slowdown on Thai Growth," IMF Working Papers 08/140, International Monetary Fund.
- Benes, Jaromir & Kevin Clinton & Roberto Garcia-Saltos & Marianne Johnson & Doug Laxton & Troy Matheson, 2010. “The Global Financial Crisis and Its Implications for Potential Output,” IMF Working Papers (forthcoming), International Monetary Fund.
- Benes, Jaromir & Papa M'B. P. N'Diaye, 2004. "A Multivariate Filter for Measuring Potential Output and the NAIRU: Application to the Czech Republic," IMF Working Papers 04/45, International Monetary Fund.
- Camen, Ulrich, 2006. "Monetary policy in Vietnam: the case of a transition country," in: “Monetary policy in Asia: approaches and implementation”, BIS Papers volume 31, pages 232-252, Bank for International Settlements.
- de Jong, P. & N. Shephard, 1995. “The simulation smoother for time series models,” Biometrika 82, 339-50.
- Doornik, J.A. (2007), Object-Oriented Matrix Programming Using Ox, 3rd ed. London: Timberlake Consultants Press and Oxford: www.doornik.com
- Edwards, Sebastian & Fernando Lefort, 1998. "Stabilization, Persistence, and Inflationary Convergence: A Comparative Analysis," Working Papers Central Bank of Chile 37, Central Bank of Chile.
- Fruhwirth-Schnatter, S., 1994. “Data augmentation and dynamic linear models,” J. Time Series Analysis 15, 183-202.
- Kaiser, Regina and Agust ́ın Maravall, 2001. Measuring Business Cycles in Economic Time Series, Lecture Notes in Statistics 154, New York: SpringerVerlag.
- Karam, Philippe D & Douglas Laxton & Andrew Berg, 2006a. "Practical Model-Based Monetary Policy Analysis--A How-To Guide," IMF Working Papers 06/81, International Monetary Fund.
- Karam, Philippe D & Douglas Laxton & Andrew Berg, 2006b. "A Practical Model-Based Approach to Monetary Policy Analysis--Overview," IMF Working Papers 06/80, International Monetary Fund.
- Kichian, M., 1999. “Measuring potential output with a state-Space framework”, Working Paper 99-9, Bank of Canada.
- Koopman, Siem Jan & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
- Kuttner, Kenneth N, 1994. "Estimating Potential Output as a Latent Variable," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 361-68, July.
- Ozbek, Levent & Umit Ozlale, 2005. “Employing the extended Kalman filter in measuring the output gap,” Journal of Economic Dynamics and Control, Volume 29, Issue 9, September 2005, Pages 1611-1622
- Planas, Christophe & Rossi, Alessandro & Fiorentini, Gabriele, 2008. "Bayesian Analysis of the Output Gap," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 18-32, January.

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10149.pdf_