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Has the forecasting performance of the Federal Reserve’s Greenbooks changed over time?

  • Ozan Ekşi , Cüneyt Orman and Bedri Kamil Onur Taş EMAIL logo
Published/Copyright: June 5, 2017
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 17 Issue 2

Abstract

We investigate how the forecasting performance of the Federal Reserve Greenbooks has changed relative to commercial forecasters between 1974 and 2009. To this end, we analyze time-variation in the Greenbook coefficients in forecast encompassing regressions. Assuming that model coefficients change continuously, we estimate unobserved components models using Bayesian inference techniques. To verify that our results do not depend on the specific way change is modeled, we also allow the coefficients to change discretely rather than continuously and test for structural breaks using classical inference techniques. We find that the Greenbook forecasts have been consistently superior to the commercial forecasts at all horizons throughout our sample period. Although the forecasting performance gap has narrowed at more distant horizons after the early-to-mid 1980s, it remains significant.

Keywords: evaluating forecasts; Greenbook inflation forecasts; SPF inflation forecasts; time-variation in coefficients
JEL Classification: C11; E52; E43

Acknowledgement

We thank the editor, Karel Mertens, and two anonymous referees for very helpful comments and suggestions.

A Appendix

A.1 Gibbs sampling algorithm of Bayesian estimation for a time-varying parameter model

The following state-space representation provides the model with time-varying coefficients:

Yt=θtXt+εt,εt∼N(0,R),θt=θt−1+υt,υt∼N(0,Q),

R and Q are the unknown parameters in the observation equation and in the transition equation, respectively. The state variable θt is also unknown and to be estimated. Since the distributions of the unknown parameters and state variable depend on each other, we employ the Gibbs algorithm which iteratively draws parameters and unobserved states conditional on each other. We run the algorithm for 12,000 replications, with 10,000 burn-in replications discarded and 2000 replications retained. The specific steps of the algorithm are briefly explained below. For further details, we refer the readers to Blake and Mumtaz (2012) .

Step 1: Initialization.

To start Gibbs sampling, we assign initialization values to unknown parameters (R and Q) of the state space model. These are set using the OLS estimates of the observation equation by using the pre-sample data from 1974:Q4 to 1978:Q2. The initial value of Q is set by using the variance of θt from this estimation.

Step 2: Sample θ conditional on R and Q using the Carter and Kohn (1994) algorithm.

Given Yt, Xt, and the initial values of R and Q, we run the Kalman filter to obtain the likelihood of the state vector. To initiate this filter, we use the OLS estimate of θ from the same pre-sample data in Step 1. To initiate the covariance matrix of θ, we multiply its estimate from the pre-sample data by T0*3.5*10 – 4, where T0 is the length of the pre-sample data, and 3.5*10 – 4 is a small number that is used to adjust for the fact that the training sample is typically short and the resulting estimates may be imprecise.[16]

The model is a linear Gaussian state space model. Assuming that the prior distribution for θ0, denoted by p(θ0), is Gaussian, the conditional posterior distribution of p(θt/yt, R, Q) is also Gaussian. A forward recursion using the Kalman filter provides expressions for posterior means and the covariance matrix:

p(θt/yt,R,Q)=N(θt/t,Pt/t),Pt/t−1=Pt−1/t−1+Q,Kt=Pt/t−1Xt(X′tPt/t−1Xt+R)−1,θt/t=θt/t−1+Kt(yt−X′tθt/t−1),Pt/t=Pt/t−1−KtX′tPt/t−1.

Starting from θT/T and PT/T, we use the Kalman filter updating equations to characterize posterior distributions of p(θT/yT, R, Q):

p(θt/θt+1,yT,R,Q)=N(θt/t+1,Pt/t+1),θt/t+1=θt/t+Pt/t(Pt/t+Q)−1(θt+1−θt/t),Pt/t+1=Pt/t−Pt/t(Pt/t+Q)−1Pt/t.

We use these equations to obtain draws of the state variable from its conditional distribution on the rest of the model parameters. That is, we generate a random trajectory for θT = (= [θ1, …, θT]) using the backward recursion starting with a draw of θT from 𝒩(θT/T, PT/T) as suggested by Carter and Kohn (1994) .

Step 3: Sample QQQ from the inverse Wishart distribution.

Conditional on a realization for θT, innovations in the coefficients, vt, are observable. Assuming an inverse-Wishart for the prior distribution of Q, with scale matrix Q0 and degree of freedom T0, its posterior distribution is also inverse-Wishart:

p(Q/yT,θT)=IW(Q1−1,T1),Q1=Q0+∑t=1Tvtv′t,T1=T0+T.

Given that Q0 and T0 are defined as the parameters governing the prior distribution of the variance of the transition equation, these equations suggest that this prior distribution is convolved with likelihood to obtain posterior distribution of Q.

Step 4: Sample RRR from the inverse Gamma distribution.

Conditional on a realization for θT, residuals from the time-varying regression are observable. Assuming the inverse-Gamma for prior distribution of R, with scale parameter R0 and degree of freedom T0, the posterior distribution is also inverse-Gamma:

p(R/yT,θT)=IG(T1/2,1/(2R1)),1/R1=(1/R0+∑t=1Tεtε′t)/2,T1=(T0+T)/2.

where R0 is the OLS estimate of R from the pre-sample data. Hence, the parameters of the prior distribution of R are also taken from the OLS estimate of pre-sample data.

Step 5: Posterior Inference.

Go back to step 1 and generate new draws of θT, R, and Q. Repeat this M0 + M1 times and discard the initial M0 draws. Use the remaining M1 draws for posterior inference.

A.2 Robustness analysis with CPI inflation forecasts

Table 4:

CPI inflation forecasting performances of the Greenbook and the SPF πh,t=β0+β1πh,tGB+β2πh,tSPF+εh,t

Forecast horizon
01234
β00.07360.9591.2481.6631.816
(0.158)(0.440)**(0.819)(0.745)**(0.567)***
β10.9271.046–0.1320.5030.958
(0.067)***(0.199)***(0.563)(0.444)(0.459)**
β20.0115–0.3860.649–0.0783–0.539
(0.083)(0.238)(0.707)(0.542)(0.414)
N110110110110110
R20.920.450.070.080.10

  1. πh,t denotes the actual inflation rate and πh,tGB and πh,tSPF denote, respectively, the Greenbook and SPF inflation forecasts. Standard errors are in parentheses. ** and *** denote significance at the 5 and 1 percent levels, respectively.

Figure 4: Time-varying coefficients on the Greenbook forecasts of CPI inflation.Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.
Figure 4:

Time-varying coefficients on the Greenbook forecasts of CPI inflation.

Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.

Figure 5: Time-varying coefficients on the SPF forecasts of CPI inflation.Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.
Figure 5:

Time-varying coefficients on the SPF forecasts of CPI inflation.

Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.

A.3 Robustness analysis with GNP growth forecasts

Table 5:

Forecasting performances of the Greenbook and the SPF in forecasting GNP growth Δyh,t=β0+β1Δyh,tGB+β2Δyh,tSPF+εh,t.

Forecast horizon
01234
β00.2380.6151.3321.4590.453
(0.545)(0.766)(0.985)(1.183)(1.217)
β10.880.9330.7940.5410.956
(0.179)***(0.23)***(0.233)***(0.246)**(0.271)***
β20.06–0.061.332–0.063–0.083
(0.131)(0.162)(0.985)(0.157)(0.121)
N141141141141137
R20.480.280.130.050.14

  1. Δy denotes the actual real GNP growth rate and Δyh,tGB and Δyh,tSPF denote, respectively, the Greenbook and SPF forecasts for real GNP growth. Standard errors are in parentheses. ** and *** denote significance at the 5 and 1 percent levels, respectively.

Figure 6: Time-varying coefficients of Greenbook forecasts of Real GNP.Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.
Figure 6:

Time-varying coefficients of Greenbook forecasts of Real GNP.

Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.

Figure 7: Time-varying coefficients of SPF forecasts of Real GNP.Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.
Figure 7:

Time-varying coefficients of SPF forecasts of Real GNP.

Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.

A.4 Robustness analysis with Federal Reserve at a timing disadvantage

Table A.III:

Forecasting performances of the Greenbook and the SPF with Federal Reserve at a timing disadvantage πh,t=β0+β1πh+1,t−1GB+β2πh,tSPF+εh,t.

Forecast horizon
01234
β00.5000.4270.4550.3950.674
(1.35)(1.20)(1.00)(0.82)(1.34)
β10.5980.4710.8770.7720.679
(3.84)**(2.30)*(4.45)**(3.02)**(2.64)**
β20.2730.4160.4550.3950.130
(1.39)(1.83)(1.00)(0.82)(0.46)
N131131131131112
R20.590.570.560.520.42

  1. πh, t denotes the actual inflation rate and πh,tGB and πh,tSPF denote, respectively, the Greenbook and SPF inflation forecasts. t-statistics are in parentheses. ** and *** denote significance at the 5 and 1 percent levels, respectively.

Figure 8: Time-varying coefficients of Greenbook forecasts with Federal Reserve at a timing disadvantage.Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.
Figure 8:

Time-varying coefficients of Greenbook forecasts with Federal Reserve at a timing disadvantage.

Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.

Figure 9: Time-varying coefficients of SPF forecasts with Federal Reserve at a timing disadvantage.Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.
Figure 9:

Time-varying coefficients of SPF forecasts with Federal Reserve at a timing disadvantage.

Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.

A.5 Robustness analysis with monthly data

Table 6:

Forecasting performances of the Greenbook and the SPF with monthly data πh,t=β0+β1πh+1,t−1GB+β2πh,tSPF+εh,t.

Forecast horizon
01234
β0–0.087–0.333–0.532–0.587–0.266
(0.354)(0.415)(0.462)(0.611)(0.600)
β10.9290.9430.9340.9771.007
(0.052)**(0.052)**(0.109)**(0.173)**(0.232)**
β20.0270.0430.07–0.5870.006
(0.067)(0.066)(0.087)(0.611)(0.139)
N9595959593
R20.860.860.760.710.64

  1. πh,t denotes the actual inflation rate and πh,tGB and πh,tSPF denote, respectively, the Greenbook and SPF inflation forecasts. Standard errors are in parentheses. ** and *** denote significance at the 5 and 1 percent levels, respectively.

Figure 10: Time-varying coefficients of Greenbook forecasts with monthly matched data.Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.
Figure 10:

Time-varying coefficients of Greenbook forecasts with monthly matched data.

Note: Time-varying Greenbook coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The sample runs from 1985:Q4 to 2009:Q4.

Figure 11: Time-varying coefficients of SPF forecasts with monthly matched data.Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.
Figure 11:

Time-varying coefficients of SPF forecasts with monthly matched data.

Note: Time-varying SPF coefficients are computed by Bayesian estimation with Kalman filtering and Gibbs sampling algorithm. 68 and 90 percent credible intervals are displayed. The procedure uses the 1974:Q4–1978:Q2 data to set priors and initial values. As a result, the sample runs from 1978:Q3 to 2009:Q4.

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Published Online: 2017-6-5

©2017 Walter de Gruyter GmbH, Berlin/Boston

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  2. Does microfinance reduce poverty? Some international evidence
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  4. Democracy and income: taking parameter heterogeneity and cross-country dependency into account
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  10. Has the forecasting performance of the Federal Reserve’s Greenbooks changed over time?
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https://doi.org/10.1515/bejm-2016-0130
Keywords for this article
evaluating forecasts; Greenbook inflation forecasts; SPF inflation forecasts; time-variation in coefficients

Articles in the same Issue

  1. Advances
  2. Does microfinance reduce poverty? Some international evidence
  3. Exchange rate policy and the role of non-traded goods prices in real exchange rate fluctuations
  4. Democracy and income: taking parameter heterogeneity and cross-country dependency into account
  5. Pass-through of imported input prices to domestic producer prices: evidence from sector-level data
  6. Economic policy uncertainty and household inflation uncertainty
  7. Corruption, fiscal policy, and growth: a unified approach
  8. Monetary policy and energy price shocks
  9. Government education expenditures and economic growth: a meta-analysis
  10. Has the forecasting performance of the Federal Reserve’s Greenbooks changed over time?
  11. Life-cycle consumption, precautionary saving, and risk sharing: an integrated analysis using household panel data
  12. Can removing the tax cap save Social Security?
  13. A non-monotonic relationship between public debt and economic growth: the effect of financial monopsony
  14. The Euler equation around the world
  15. Structural change and non-constant biased technical change
  16. Contributions
  17. Trade and growth in a model of allocative inefficiency
  18. Macroeconomic Shocks and Corporate R&D
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