Real-Time Forecasting of Inflation and Output Growth in the Presence - - PowerPoint PPT Presentation

Real-Time Forecasting of Inflation and Output Growth in the Presence of Data Revisions

Michael Clements Ana Beatriz Galvão

Warwick/Queen Mary

September 2010

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 1 / 27

Data Revisions and Real-Time Data

Data Vintages of US real output growth:

2003:Q1 2003:Q2 2003:Q3 2003:Q4 2004:Q1 2004:Q2 2004:Q3 2004:Q4 2005:Q1 2005:Q2 2005:Q3 2005:Q4 2002:01 1.23 1.23 1.23 1.23 1.15 1.15 0.84 0.84 0.84 0.84 0.68 0.68 2002:02 0.31 0.31 0.31 0.31 0.47 0.47 0.59 0.59 0.59 0.59 0.54 0.54 2002:03 0.99 0.99 0.99 0.99 0.83 0.83 0.64 0.64 0.64 0.64 0.59 0.59 2002:04 0.19 0.34 0.34 0.34 0.32 0.32 0.18 0.18 0.18 0.18 0.05 0.05 2003:01 . 0.40 0.35 0.35 0.49 0.49 0.48 0.48 0.48 0.48 0.42 0.42 2003:02 . . 0.59 0.81 0.76 0.76 1.01 1.01 1.01 1.01 0.90 0.90 2003:03 . . . 1.73 1.97 1.97 1.79 1.79 1.79 1.79 1.75 1.75 2003:04 . . . . 0.99 1.01 1.03 1.03 1.03 1.03 0.88 0.88 2004:01 . . . . . 1.02 1.10 1.10 1.10 1.10 1.04 1.04 2004:02 . . . . . . 0.75 0.81 0.81 0.81 0.86 0.86 2004:03 . . . . . . . 0.91 0.98 0.98 0.97 0.97 2004:04 . . . . . . . . 0.77 0.94 0.81 0.81 2005:01 . . . . . . . . . 0.76 0.93 0.93 2005:02 . . . . . . . . . . 0.84 0.81 2005:03 . . . . . . . . . . . 0.93 Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 2 / 27

Data Revisions on Output Growth and Inflation

Mean Standard Deviation Autocorrelation (1st)

1 + t t

y

14 + t t

y

1 09Q t

y

1 + t t

y

14 + t t

y

1 09Q t

y

1 + t t

y

14 + t t

y

1 09Q t

y

Output growth 1965Q3-1985Q2 0.76 0.79 0.81 1.08 1.07 1.08 0.28 0.29 0.29 1985Q3-2006:Q4 0.68 0.68 0.75 0.43 0.52 0.50 0.33 0.33 0.23 GDP Deflator 1965Q3-1985Q2 1.45 1.43 1.41 0.59 0.59 0.59 0.70 0.75 0.80 1985Q3-2006:Q4 0.58 0.65 0.60 0.28 0.27 0.23 0.57 0.55 0.56 PCE Deflator 1965Q3-1985Q2 1.40 1.39 1.38 0.63 0.64 0.65 0.83 0.83 0.84 1985Q3-2006:Q4 0.64 0.69 0.64 0.38 0.35 0.30 0.49 0.60 0.56

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 3 / 27

Real-Time Data and Forecasting I

• The use of ‘final-revised’ data may exaggerate the predictive

power of explanatory variables to what could have been achieved at the time using the then available data (‘real-time data’): Diebold and Rudebush (1991), Robertson and Tallman (1998), Orphanides (2001), Croushore and Stark (2001, 2003), Faust, Rogers and Wright (2003), and Orphanides and van Norden (2005).

This paper: what is the best way (minimises mean squared error) of incorporating data vintages in real-time forecasting

• f output growth and inflation with AR and ADL models?

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 4 / 27

Real-Time Data and Forecasting II

Ways of organizing data vintages for real-time forecasting:

1 Use the values from the latest available vintage of data to estimate

the forecasting model: end-of-sample vintage approach - EOS data (Koenig, Dolmas and Piger, 2003).

2 Vintages are incorporated such that the forecasting model is

estimated with data that mimics the vintage-data structure on the real-time forecast loss function - RTV (real-time vintage) data.

• For example, if forecasts of yT+2

T+1 are computed using two lags yT+1 T

and yT+1

T−1, then the forecast model should be estimated using yt+1 t

• n the LHS and yt

t−1 and yt t−2 on RHS with both vintage

(superscript) and observed date (subscript) varying from t = 2 up to t = T.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 5 / 27

Real-Time Data and Data Revisions I

• We are able to show that the use of EOS data to estimate AR

forecasting models delivers estimates that do not minimise the real-time mean squared forecast error.

• If RTV data is employed instead, we are able to obtain consistent

estimates of the optimal AR coefficients, that is, the values that minimise the population MSE.

• The implications of the use of EOS instead of RTV data are based
• n a model of the data revision process.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 6 / 27

Real-Time Data and Data Revisions II

• Many authors have build models to characterize the dynamics of

data revisions (Harvey et al, 1983; Howrey, 1984, Sargent, 1989; Patterson, 1995; Cunningham et al, 2007; Jacobs and van Norden, 2007).

• Instead of using a model of data revisions to measure the ‘true

data’, we use the model to establish how revisions characteristics affect the optimal way of organizing real-time data, that is, how large are MSE differences between RTV and EOS data.

• In this paper, we use a model that decomposes the observed data

into true underlying value, and data revisions that add news and noise (Jacobs and van Norden, 2007).

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 7 / 27

Implications: RTV versus EOS data

• The gains from the use of RTV instead of EOS data to estimate AR

forecasting models depend on how large are the variances of data revisions in comparison to the variance of the underlying data, and also how the revisions’ variances decay with each data revision.

• The gains are larger when the estimation sample is small and

revisions primarily add news, and the underlying process is reasonable persistent. Relative MSE ratios are measured with a monte carlo exercise using the model of data revisions calibrated to

• utput growth and inflation revisions.
• Even when considering a model of data revisions based on a VAR
• f multiple vintages estimated to macro data, monte carlo results

also suggest MSE gains of around 2-3%.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 8 / 27

Forecasting output growth and inflation

• When forecasting output growth and inflation in the 1985-2008

period, the use RTV data improves forecasts of AR models with EOS data in around 1-4% of RMSFE.

• When adding economic indicators, which are also subject to data

revisions, to the forecasting model (ADL), the use of RTV data reduces RMSFE up to 8% (larger gains when nowcasting and using data from 1980 onwards in the estimation).

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 9 / 27

Statistical Framework I

• Observed data estimates: yt=
• yt+1

t

, . . . , yt+l

t

• ; True value:

yt

• Noise revisions: εt =
• εt+1

t

, . . . , εt+l

t

• ; Cov
• εt+s

t

, yt = 0

• News revisions: vt =
• vt+1

t

, . . . , vt+l

t

• ; Cov
• vt+s

t

, yt+s

t

= 0 yt = i yt + vt + εt

• yt = ρ0 +

p

∑

i=1

ρi yt−i + R1η1t

underlying

+

l

∑

i=1

σviη2t,i

news

vt= −        σv1 σv2 . . . σvl σv2

...

σvl              η2t,1 η2t,2 η2t,l       ;εt=       σε1η3t,1 σε2η3t,2 σεlη3t,l      

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 10 / 27

Statistical Framework II

• The Statistical Model is modified to allow for revisions that have

non-zero mean such that they change the unconditional mean of

• yt when they add news.
• The model can be also modified to accommodate the periodic

pattern of BEA annual revisions (published in July) together with the revision pattern from ‘advance’ estimates yt+1

t

up to ‘final’ estimates yt+2

t

.

• Even though our analytical results are for this specific statistical

framework, the implications are general since our main requirement is stationarity of the underlying yt and the revision

• processes. We also exploit a data revision processes based on a

VAR model in the monte carlo evaluation.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 11 / 27

Optimal AR Parameters in Population I

• Parameters that minimise the real-time quadratic loss function.
• Forecasts are computed using the latest available data from the

T + 1 vintage: yT+1

T

=

• yT+1

T

, yT+1

T−1, . . . , yT+1 T−p+1

• .
• The optimal parameters are the ones that solve:

(φ∗

0, φ∗) = arg min

• yT+1+f

T+1

− φ0 − φyT+1

T

2 , that are: φ∗ =

• Σ

y + Σv + Σ yv + Σ

• yv + Σε

−1 Σ

y + Σ

• yv
• ρ

φ∗ =

• 1 − φ∗i
• µ

y

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 12 / 27

Optimal AR Parameters in Population II

when the processes of data revisions is described by the statistical framework.

• The optimal parameters depend on how large are the news/noise

revisions second moments (Σv, Σε) in comparison with the true data second moment (Σ

y).

• For example, if the "great moderation" has reduced the variation
• f "true" output growth, but has a smaller impact on the variation
• f the data revisions, then the impact of the "great moderation" is

to enlarge the distance between φ∗ and ρ.

• When data revisions are non-zero mean, the optimal value of the

intercept changes to: φ∗

0 =

• 1 − φ∗i
• µ

y + µv1 + µε1 − φ∗µε − φ∗µv,

that is, it depends on mean of news (µv1 − φ∗µv) and noise (µε1 − φ∗µv) revisions.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 13 / 27

AR Parameters estimated with EOS data I

• The AR(p) with EOS data is:

YT+1 = iα0 + Y−1α + error YT+1 =

• yT+1

p+1, . . . , yT+1 T−1, yT+1 T

• , YT+1

−i

=

• yT+1

p+1−i, . . . , yT+1 T−i−1, yT+1 T−i

• When OLS is applied to an AR(p) with EOS data and data

revisions are described by the statistical framework, the large sample estimates are: α∗ =

• Σ

y + Σv + Σ yv + Σ

• yv + Σε

−1 Σ

y + Σ

• yv
• ρ

α∗ =

• 1 − α∗i
• µ

y,

where the second moment matrices Σv and Σε differ from Σv and Σε.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 14 / 27

AR Parameters estimated with EOS data II

• Intuitively, when the sample is large, the use of EOS data amounts

to mainly using fully-revised data (i.e., data from the yt+l

t

vintage) whilst optimal forecasts are obtained by relating the first estimates

• f the LHS variable to early estimates of the RHS variables.
• The finding of the lack of optimality of forecasts computed with

AR model estimated with EOS data holds for news and noise revisions, although forecasts are unbiased when the data revisions are zero mean.

• When revisions are non-zero mean, forecasts are also biased.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 15 / 27

AR Parameters estimated with RTV data I

• The AR(p) with RTV data is:

Yt = iβ0 + Yt

−1β + error

Yt =

• yp+2

p+1, . . . , yT T−1, yT+1 T

• ,

Yt

−i =

• yp+1

p+1−i, . . . , yT−1 T−i−1, yT T−i

• ,

i =

• When OLS is applied to an AR(p) with RTV data and data

revisions are described by the statistical framework, the large sample estimates are: β∗

0= φ∗; β∗ = φ∗ 0.

• The forecasts computed with RTV data to estimate the AR(p)

model are optimal because they satisfy E

• yt+1

t

− β0 − βyt

t−1

= 0 and yt+1

t

and yt

t−1 are in-sample representations of the forecasting

loss function that includes yT+2

T+1 and yT+1 T

.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 16 / 27

AR Parameters estimated with RTV data II

• When the mean of data revisions are non-zero, forecasts obtained

with RTV data are non-biased for first released data (f = 1), but the model of data revisions suggest a simple computation for the bias when f > 1.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 17 / 27

RTV versus EOS data: using analytical results I

• Computation of α∗, φ∗, MSEEOS, MSEOPT and forecast biases with

an AR(2) assuming pure news and pure noise.

• Underlying process with low (sum(ρ) = .4) and high persistence

(sum(ρ) = .8). Four different decay patterns for σvi and σεi, including one that t + l vintage reveals true data, calibrated to US macro data. l = 14.

• The impact of data revisions is larger for more persistent data and

there are marked differences between α∗ and β∗ for individual coefficients, but not for the sum of AR parameters.

• The loss in terms of MSFE from EOS estimation in comparison

with optimal forecasting is in the 2-3% range for more persistent data.

• Under noise, EOS is more heavily penalized when the variance of

the first revision is large relative to subsequent revisions.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 18 / 27

RTV versus EOS data: using analytical results II

• Under news, larger penalization depends on the sum of the

revisions variances ∑l

i=1 σvi.

• Usual gains from RTV data are still observed when the last

vintage yt+l

t

reveals true data.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 19 / 27

VAR of multiple Vintages

• A vector of q estimates of y: zt−i =
• yt−i

t−1−i, yt−i t−2−i, . . . , yt−i t−q−i

• zt = c0 +

p

∑

i=1

Γizt−i + εt

• The model is augmented to incorporate the effect of benchmark

revisions by including dummies that affect c0, and dynamics is restricted to accommodate the seasonality of the BEA data revisions (SVB-VAR).

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 20 / 27

RTV versus EOS data: small sample simulation

Forecasting

1 1 1 + + + T T

y

Forecasting

1 4 4 + + + T T

y

DGP n. MSFE Ratio Asym. T=50 T=100 T=50 T=100 Under Noise 1 0.993 1.001 1.001 1.006 0.998 2 0.994 1.004 1.002 1.014 0.999 3 0.996 0.994 0.999 0.995 0.995 4 0.993 1.002 1.000 1.003 0.997 5 0.981 0.990 0.986 1.010 1.004 6 0.965 0.981 0.974 1.015 1.009 7 0.988 0.981 0.990 0.998 1.001 8 0.978 0.991 0.984 0.994 1.009 Under News 1 0.992 0.976 0.982 0.966 0.979 2 0.992 0.947 0.966 0.945 0.969 3 0.989 0.965 0.978 0.955 0.976 4 0.992 0.976 0.985 0.968 0.981 5 0.973 0.949 0.959 0.964 0.976 6 0.955 0.926 0.941 0.958 0.968 7 0.951 0.925 0.929 0.971 0.975 8 0.972 0.941 0.957 0.954 0.981 SVB-VAR as DGP 9 0.971 0.970 0.995 0.994 10 0.983 0.987 0.982 0.971 11 0.986 0.991 0.994 0.980

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 21 / 27

Forecasting Output Growth: AR and VB-VAR

• Out-of-sample period: 1985:Q3-2008:Q4, n = 94. ratio RMSFE:

RTV/EOS.

• VB-VAR: a VAR of multiple vintages with q estimates.

h = 1 h = 4

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y +

1 4 4 + + + T T

y

14 4 4 + + + T T

y

1 09 4 Q T

y

+

AR(1) 0.976 0.981 0.999 0.956 0.956 0.972 0.998 0.995 0.982 0.980 VB-VAR(1), q=4 0.999 0.996 1.013 0.965 0.965 0.988 VB-VAR(1), q=5 0.995 0.996 1.012 0.967 0.960 0.980 VB-VAR(1), q=8 0.994 0.986 1.009 1.002 0.958 0.989 VB-VAR(1), q=14 1.028 1.026 1.034 1.017 0.970 0.990

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 22 / 27

Forecasting Inflation: AR and VB-VAR

• GDP deflator RMSFE, ratio RTV/EOS:

h = 1 h = 4

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y

+ 1 4 4 + + + T T

y

14 4 4 + + + T T

y

1 09 4 Q T

y

+

AR(4) 0.961 0.972 0.959 0.959 0.967 0.953 0.973 0.977 0.994 0.991 VB-VAR(1), q=4 0.962 0.962 0.958 0.968 0.966 0.958 VB-VAR(1), q=5 0.988 0.966 0.965 1.034 1.028 1.021 VB-VAR(1), q=8 0.963 0.956 0.955 1.036 1.040 1.027 VB-VAR(1), q=14 0.955 0.953 0.959 0.973 0.978 0.970

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 23 / 27

ADL models of output

• Target: yt+h = 400(ln(Xt+h) − ln(Xt+h−1)).
• The RHS vintages with RTV data change with h : h = 0,

xt+1

t

, yt

t−1; h = 4, xt−3 t−4, yt−3 t−4 (LHS is yt+1 t

). Direct forecasts.

h = 0 h = 1 h = 4

Ratio AR(1)_RTV Ratio AR(1)_RTV Ratio AR(1)_RTV Model: sample

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y +

1 09 1 Q T

y +

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y +

1 09 1 Q T

y +

1 4 4 + + + T T

y

14 4 4 + + + T T

y

1 09 4 Q T

y +

1 09 4 Q T

y +

starts: With industrial production DL (2) 1959:Q1 1.026 1.001 1.000 0.847 0.999 0.992 0.996 0.974 ADL (1,2) 1959:Q1 1.025 1.004 1.009 0.855 1.052 1.038 1.052 1.027 0.972 0.975 0.997 1.052 DL (2) 1979:Q1 0.943 0.945 0.953 0.838 0.984 0.983 0.986 0.991 ADL (1,2) 1979:Q1 0.921 0.958 0.928 0.850 0.971 0.980 0.981 0.990 0.936 0.964 0.982 1.001 With employment DL (2) 1959:Q1 1.022 1.010 0.998 0.895 0.990 0.993 0.998 0.994 ADL (1,2) 1959:Q1 0.983 1.013 1.011 0.893 1.002 1.043 1.045 1.042 1.014 1.013 1.024 1.131 DL (2) 1979:Q1 0.949 0.963 0.975 0.888 0.969 0.988 0.987 1.030 ADL (1,2) 1979:Q1 0.921 0.958 0.968 0.890 0.898 0.975 0.959 1.024 0.979 0.987 1.007 1.023

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 24 / 27

ADL models of inflation

h = 0 h = 1 h = 4

Ratio AR(4)_RTV Ratio AR(4)_RTV Ratio AR(4)_RTV Model: sample

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y +

1 09 1 Q T

y +

1 1 1 + + + T T

y

15 1 + + T T

y

1 09 1 Q T

y +

1 09 1 Q T

y +

1 4 4 + + + T T

y

14 4 4 + + + T T

y

1 09 4 Q T

y +

1 09 4 Q T

y +

starts: With industrial production ADL (4,2) 1959:Q1 0.948 0.945 0.945 1.001 0.945 0.958 0.943 0.985 1.052 1.006 0.983 1.044 ADL (4,2) 1979:Q1 0.935 0.911 0.940 0.992 0.915 0.899 0.918 1.007 0.946 0.954 0.922 1.032 With employment ADL (4,2) 1959:Q1 0.952 0.974 0.967 1.027 0.968 0.986 0.968 1.016 0.990 1.017 0.983 1.103 ADL (4,2) 1979:Q1 0.940 0.905 0.945 0.996 0.939 0.913 0.926 0.999 0.965 0.976 0.948 1.063 With output growth ADL (4,2) 1959:Q1 0.949 0.944 0.939 0.997 0.953 0.974 0.953 0.979 0.962 1.037 0.972 0.968 ADL (4,2) 1979:Q1 0.955 0.926 0.958 1.013 0.933 0.911 0.928 1.015 0.958 0.979 0.943 1.049

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 25 / 27

Summary I

• The use of real-time vintage data instead of end-of-sample data to

estimate AR models improves forecast accuracy in real time, even when the aim is to forecast final-revised data.

• Based on a model of data revisions calibrated to US model data,

we measure the size of the expected gains from using RTV instead

• f EOS for data at around 2-3% of MSFE. Larger RTV gains are

expected when sample size are small and revisions add news.

• The use of RTV data improves accuracy in forecasting US output

growth and inflation with AR models. Because AR models are common benchmark models for macroeconomic forecasting, these findings could affect measurement of predictability with economic indicators.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 26 / 27

Summary II

• Our small forecasting evaluation with ADL models indicates that

the AR benchmark is indeed hard to beat when estimated with RTV data, and that RTV data may also improve output growth and inflation forecasts with ADL models of economic indicators.

Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 27 / 27