Jan P.A.M. Jacobs, Samad Sarferaz, Jan-Egbert Sturm and Simon van Norden

Transcription

1 Jan P.A.M. Jacobs, Samad Sarferaz, Jan-Egbert Sturm Simon van ESCoE Conference on Economic Measurement London, May 2018

2 I GDP I GDP E Figure: U.S. Real GDP growth: Expenditure vs Income measures

3 II Which is the better measure of GDP? Expenditure (GDE) or Income (GDI)? Nalewaik (2012) Chang Li (2015) Reconciliation: Stone, Champernowne Meade (1942) Weale (1992) Diebold (2010) Aruoba et al (2012) FRB Philadephia publishes GDP +

4 III GDPplus GDPE GDP I Figure: Following Aruoba et al. (2015), FRB Philadelphia publish s: GDP +

5 IV GDE GDI Through the Great Recession Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q GDE - Advance GDE - 2nd Release GDE - 12th Release GDE - 24th Release GDI - 2nd Release GDI - 12th Release GDI - 24th Release Figure: Both series have important revisions

6 Problem Reconciliation relies on assumptions about the errors in the series being reconciled. which is more precise? lead/lag relationships? News or Noise? These relationships vary depending on which release(s) we consider. Important for producing efficient estimates. Important for understing reliability of estimates.

7 Our Contribution 1. We model the problem in a stard, linear state-space. (following Jacobs van JoE 2011) 2. We show how to allow for multiple data releases varying precision series dynamics combinations of news noise errors 3. Reconcile real GDE GDI growth in a real-time data environment 4. Compare our new measure (GDP ++ ) to real GDE GDI growth 5. Decompose initial estimates of GDE GDI growth into news noise shocks

8 GDP ++ 8 GDP Through the Great Recession Q Q Q Q Q Q Q Q Q Q GDE - Advance GDE - 2nd Release GDE - 12th Release GDE - 24th Release GDI - 2nd Release GDI - 12th Release GDI - 24th Release GDP ++

9 Revision properties News Noise Let y i t be the i-th release of y in period t ỹ t true value of y t 1. Noise: 2. News: y i t = ỹ t + ζ i t, cov(ỹ t, ζ i t) = 0 i revisions (partly) forecastable vintages more volatile than true values ỹ t = y i t + ν i t, cov(y i t, ν i t) = 0 i Linked to rational forecasts (De Jong 1987) rational statistical agency (Sargent 1989) revisions cannot be forecast vintages less volatile than true values

10 Notation GDP t GDE t GDI t GDPt i GDP t + GDP ++ t ν t ζ t real GDP growth ( Truth ) real GDP growth (Expenditure measure) real GDP growth (Income measure) superscript i indicates release real GDP growth - FRB Philadelphia measure (after Aruoba et al. 2015) our real GDP growth measure News measurement error Noise measurement error

11 State-Space Model I Measurement Equation: [ ] GDE L t GDIt L = [ ι ] [ ] [ ] ν L GDP t + Et ζ L νit L + Et ζit L where GDE L t = [GDE 1 t,..., GDE l t], GDI L t = [GDI 1 t,..., GDI l t], ν L Et = [ν 1 Et,..., ν l Et], ν L It = [ν 1 It,......, ν l It] ζ L Et = [ζ 1 Et,..., ζ l Et], ζ L It = [ζ 1 It,..., ζ l It], ι is a 2l 1 vector of ones. (1) News: E[ν j t GDP k t ] = 0 j > k Noise: E[ζ L t GDP t ] = 0

12 State-Space Model II Transition Equation: Let α t = [GDP t, νet L, ν L It, ζ L Et, ζ L It ] The transition equation may be compactly written as [ ] ρ 0 α t = α 0 0 t 1 + R η t, (2) 1 ι l ι l U R = 0 0 U 0 0 (3) I l I l U is upper triangular matrix of ones η t = [η Gt, η i Eνt, η i Iνt, η i Eζt, η i Iζt ] N(0, D) for a diagonal matrix D

13 Identification How can we hope to distinguish News Noise measurement errors? (2) implies that all persistence comes through GDP t. News shocks are part of GDP t, so have a persistent effect. Noise shocks are not, so must be transitory. Jacobs van (2011) consider more general news noise dynamics in the univariate case. We provide a formal proof of identification in their special case using Komunjur Ng (2011, Ectra) Kishor Koenig (2012) also identify both news noise shocks in the univariate case.

14 estimation Data Monthly vintages of quarterly series 2003Q1 2014Q3 from Bureau of Economic Analysis (BEA) For real GDE growth we use the advance, third, the 12th the 24th releases For real GDI growth we use the second/third, the 12th the 24th releases Gibbs Sampling with diffuse priors Estimate with News only, Noise only, News & Noise as expected Noise only gives less volatile GDP growth News only gives more volatile GDP growth

15 Real GDP growth dynamics GDP E GDP I < GDP ++ GDPplus ;

16 Contribution to GDP ++ t Use Kalman gain to assess importance of GDP I GDP E at different releases Table: Kalman gains GDP E GDP I Advance 0.06 Third th th Release

17 Historical decomposition of real GDE growth Total revision News Noise

18 Historical decomposition of real GDI growth Total revision News Noise

19 GDP ++ 8 GDP Through the Great Recession Q Q Q Q Q Q Q Q Q Q GDE - Advance GDE - 2nd Release GDE - 12th Release GDE - 24th Release GDI - 2nd Release GDI - 12th Release GDI - 24th Release GDP ++

20 We show how to reconcile series subject to revision due to news noise. Identification possible due to differing dynamic impact of news noise errors. We provided a new real GDP growth measure using real-time data More persistent smaller residual variance than real GDE growth real GDI growth Similar AR-coefficient but smaller residual variance than GDP + Computed historical decomposition of real GDE growth real GDP growth measurement errors Higher news share in real GDE growth than in real GDI growth 2008 downturn in GDI seems like noise rather than a leading indicator of recession.

21 GDP ++ vs. real GDE growth True value Advance Second 12th release 24th release

22 GDP ++ vs. real GDI growth True value Second/Third 12th 24th release