Can GDP measurement be further improved? Data revision and Can GDP measurement be further improved? reconciliation Jacobs, Sarferaz, Data revision and reconciliation Sturm and van Norden Motivation Jan P.A.M. Jacobs, Samad Sarferaz, Jan-Egbert Sturm and Outline Econometric Simon van Norden framework Data and Estimation Results FRB Philadelphia Conclusion October 2020 (Forthcoming, JBES )
Motivation I Can GDP measurement be further improved? Which is the better measure of GDP? Expenditure (GDE) or Income (GDI)? Data revision and reconciliation 10 Jacobs, Sarferaz, Sturm and van Norden Motivation 5 Outline GDE Econometric framework Data and 0 Estimation GDI Results Conclusion -5 -10 2000 2002 2004 2006 2008 2010 2012 2014 2016
Motivation II Can GDP measurement be further improved? Data revision Which is the better measure of GDP? Expenditure (GDE) or Income (GDI)? and reconciliation ◮ Nalewaik (2012) Jacobs, Sarferaz, Sturm and van ◮ Chang and Li (2015) Norden Motivation Outline Reconciliation: Econometric ◮ Stone, Champernowne and Meade (1942) framework Data and ◮ Weale (1992) Estimation Results ◮ Diebold (2010) Conclusion ◮ Aruoba et al (2013, 2016) ◮ FRB Philadephia publishes GDP + ◮ BEA publishes average (GDP 50 / 50 )
Motivation III Can GDP measurement be further Following Aruoba et al. (2016), FRB Philadelphia publish GDP + improved? Data revision and 6 reconciliation Jacobs, Sarferaz, Sturm and van 5 Norden GDP + Oct.2016 Motivation 4 Outline Econometric GDP + framework May2015 3 Data and Estimation Results 2 Conclusion GDP + 1 Jan.2016 0 2011 2012 2013 2014
Problem Can GDP measurement be further improved? Data revision and Reconciliation relies on assumptions about the errors in the series being reconciliation reconciled. Jacobs, Sarferaz, Sturm and van ◮ which is more precise? Norden ◮ lead/lag relationships? Motivation Outline ◮ News or Noise? Econometric ◮ Is variability due to measurement error? framework ◮ Or does it reflect useful information? Data and Estimation Results These relationships vary depending on which release(s) we consider. Conclusion ◮ Important for producing efficient estimates. ◮ Important for understanding reliability of estimates.
Our Contribution Can GDP measurement be further improved? Data revision and reconciliation 1. We model the reconciliation problem in a linear state-space framework for Jacobs, Sarferaz, Sturm and van data revision (cf Jacobs and van Norden JEconometrics 2011) Norden 2. We show how to allow for Motivation ◮ multiple data releases with varying precision Outline ◮ series dynamics Econometric framework ◮ news and noise errors, possibly correlated across the two series Data and 3. We show how use of multiple vintages can provide identification. Estimation Results 4. Compare our new measure ( GDP ++ ) to real GDE and GDI growth Conclusion 5. Decompose initial estimates of GDE and GDI growth into news and noise shocks
GDP ++ vs GDE Can GDP measurement be further improved? Data revision 10 and reconciliation 8 Jacobs, Sarferaz, Sturm and van 6 Norden Motivation 4 Outline Econometric 2 framework Data and 0 Estimation Results -2 Conclusion -4 GDP ++ Advance Second -6 12th release 24th release -8 2004 2006 2008 2010 2012 2014 2016
GDP ++ vs GDI Can GDP measurement be further improved? Data revision 12 and reconciliation 10 Jacobs, Sarferaz, Sturm and van 8 Norden 6 Motivation Outline 4 Econometric framework 2 Data and Estimation 0 Results Conclusion -2 -4 GDP ++ Second/Third -6 12th 24th release -8 2004 2006 2008 2010 2012 2014 2016
Revision properties Can GDP measurement be further News and Noise improved? Data revision Let y i and t be the i -th release of y in period t and ˜ y t ≡ ‘true’ value of y t reconciliation Jacobs, Sarferaz, Sturm and van 1. Noise: Norden y i y t + ζ i y t , ζ i t = ˜ cov (˜ t ) = 0 ∀ i t , Motivation ⇒ revisions (partly) forecastable Outline Econometric ⇒ vintages more volatile than ‘true’ values framework 2. News: Data and Estimation y t = y i t + ν i cov ( y i t , ν i ˜ t , t ) = 0 ∀ i Results Conclusion Linked to rational forecasts (De Jong 1987) rational statistical agency (Sargent 1989) ⇒ revisions cannot be forecast ⇒ vintages less volatile than “true” values
Notation Can GDP measurement be further improved? Data revision real GDP growth (“Truth”) GDP t and reconciliation GDE t real GDP growth (Expenditure measure) Jacobs, Sarferaz, real GDP growth (Income measure) GDI t Sturm and van Norden superscript i indicates release GDE i Motivation t Outline GDP + real GDP growth - FRB Philadelphia measure t Econometric framework (after Aruoba et al. 2016) Data and GDP ++ our real GDP growth measure Estimation t Results News measurement error ν t Conclusion ζ t Noise measurement error
State-Space Model I Can GDP measurement be further Measurement Equation: improved? Data revision and � GDE L � ν L � ζ L � � � reconciliation t Et Et = GDP t + + (1) GDI L ν L ζ L Jacobs, Sarferaz, t It It Sturm and van Norden Data = Truth + News + Noise Motivation where Outline Econometric framework GDP t is a latent variable Data and Estimation GDE L t , . . . , GDE l GDI L t , . . . , GDI l t = [ GDE 1 t = [ GDI 1 t ] ′ , t ] ′ , Results ν L Et , . . . , ν l ν L It , . . . ..., ν l Et = [ ν 1 It = [ ν 1 Et ] ′ , It ] ′ Conclusion ζ L Et = [ ζ 1 Et , ..., ζ l ζ L It = [ ζ 1 It , ..., ζ l Et ] ′ , It ] ′ , News: E [ ν j t ] = 0 = E [ ν j E,t | GDE k I,t | GDI k t ] ∀ j > k Noise: E [ ζ j i,t | GDP t ] = 0 ∀ i = { E, I } j = 1 , . . . , L
State-Space Model II Can GDP measurement be further improved? Transition Equation: Data revision and α t = T · α t − 1 + R · η t (2) reconciliation ′ , ν L ′ , ζ L ′ , ζ L ′ ] ′ Jacobs, Sarferaz, where α t = [ GDP t , ν L Sturm and van Et It Et It Norden Identification results from restrictions on the T and R matrices. Motivation Outline ◮ T has one non-zero element ρ to capture persistence in GDP t , and Econometric framework Data and R 2 + R 3 R 1 0 0 Estimation − V l · diag( R 1 ) − V l · diag( R 3 ) 0 0 Results R = − V l · diag( R 2 ) (3) 0 0 0 Conclusion 0 0 R 4 R 6 R 5 0 0 0 where R 1 , . . . , R 6 are l × 1 vectors of σ ’s and V l is an l × l matix with 1’s above the diagonal.
Identification Can GDP measurement be further improved? In a model with l releases of each series Data revision and ◮ we have l · (2 l + 3) moments reconciliation ◮ to estimate 1 + 6 l parameters ( ρ and R 1 , . . . , R 6 ) Jacobs, Sarferaz, Sturm and van Norden Releases Moments Parameters Identified? Motivation l = 1 5 7 No Outline l = 2 14 13 Yes Econometric framework l = 3 27 19 Yes Data and Estimation l = 4 44 25 Yes Results Formal proof follows Komunjer and Ng (2011). Conclusion Restrictions on T imply that all serial persistence comes through GDP t . ◮ News shocks are part of GDP t , and so have a persistent effect. ◮ The behavior of News across releases is tightly restricted (via V l .)
Data and estimation Can GDP measurement be further improved? Data revision and Data reconciliation ◮ Monthly vintages of quarterly series 2002Q4–2017Q1 Jacobs, Sarferaz, Sturm and van (earliest available first releases for GDI) Norden ◮ For real GDE growth Motivation Outline we use the advance, third, the 12th and the 24th releases Econometric ◮ For real GDI growth framework Data and we use the second/third, the 12th and the 24th releases Estimation Results Estimation Conclusion ◮ Gibbs Sampling with diffuse priors ◮ Estimate with and without shocks correlated across GDI & GDE
Real GDP growth dynamics Can GDP measurement be further improved? Data revision 9 and reconciliation 8 Jacobs, Sarferaz, Sturm and van Norden 7 Motivation GDI Outline 6 Econometric framework 2 Data and GDE 5 Estimation Results GDP 50/50 4 Conclusion GDP ++ ++ GDP + GDP uncorr 3 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Contribution to GDP ++ Can GDP t measurement be further improved? Data revision ◮ Use Kalman gain to assess importance of GDP I and GDP E at different and reconciliation releases Jacobs, Sarferaz, Sturm and van Norden Table: Kalman Gains Motivation Outline Balanced Sample Ragged-Edge Sample Econometric framework Weight on GDE GDI GDE GDI Data and Estimation News and Noise Results Advance 0.0272 0.2311 Conclusion Second/Third -0.2103 0.3067 0.3363 0.4804 12th 0.7104 0.1081 0 0 24th Release 0.0479 0.0125 0 0
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