Outline Introduction Theory Empirical Conclusions
Permanent vs Transitory Components and Economic Fundamentals Anthony Garratt, Donald Robertson, Stephen Wright Yang Haoxi WISE, Xiamen University
Octorber 8th, 2008
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Abstract I
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Any non-stationary series can be decomposed into permanent(or ”trend”) and transitory(or ”cycle”) components. Typically some atheoretic pre-flitering procedure, extract the permanent component. New derivation of multivariate Beveridge-Nelson permanent and transitory components,the latter reflect deep economic uncertainty. Analysis fundamental underlying stationary processes.Far clearer economic interpretations.Combine economic fundamental and techniques.
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Outline
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Introduction B-N Trends in Cointergration VAR Model Empirical Illstrations I I
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Valuation Indicators and the US Stock Market A Small Model of the UK Economy
Conclusion Q and A
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Traditional Approach
Macroeconomic analysis is largely formulated in terms of stationary processes. Traditionaly and normal a trend of macroeconomic variate is extracted by some pre-filtering procedure.”Detrend” is a ”black box” process.
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Object and Theory in the Paper I
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Object: To show that the process that generates B-N trends is visible which can be derived from VAR representation. Transitory components can be related to the stationary processes of the underlying observable. Process: 1.Look for underlying stationary process 2.Identify predictive power of stationary process Practical Questions: Cointegration and Sensitivity to the Assumption Interpretation: Adjustment of Disequilibrium and Economic Fundamental
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
B-N Trends Denotes the B-N trends
xˆt = lim Et xt+h − gh h→∞
(1)
If 4xt gives a stationary MA representation
4xt = g + C(L)εt
(2)
4xˆt = g + C(1)εt
(3)
then the B-N trends is
suppose we take any xt into permanent and transitory components
xt = xP t + xT t Anthony Garratt, Donald Robertson, Stephen Wright
(4)
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
B-N Trends
since the transitory components satisfy lim Et xT t+h = 0
(5)
lim Et xP t+h = xˆt
(6)
h→∞
then we have h→∞
All possible permanent components must converge in expectation on B-N trends as the forecast horizon increases.
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Forecastion from a Cointegrating VAR A cointegrating VAR in n variables of rank r 0
4xt = Ψ + αβ xt−1 + Φ4xt−1 + εt
(7)
equivalently: whereg κ are the trend growth rates in the variables 0
4xt = g + α(β xt−1 − κ) + Φ(4xt−1 − g) + εt
(8)
0
β xt is typically assumed to pick out cointegration ralationships, solving for the steady state 0
Et xt = xt + gh + αh (β xt − κ) + Φh (4xt − g)
(9)
infinite horizon error correction representation 0
lim (Et xt − gh) = xt + α∞ (β xt − κ) + Φ∞ (4xt − g) (10) infinite horizon represontation all disequilibria must in expectation be fully eliminated depends on the matrices α∞ β∞ Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
B-N Trends as Conditional Cointegrating Equilibrium Value combining (1) and (10),trend values always satisfy cointegration equilibrium 0
β xˆt = κ
0
xt − xˆt = −α∞ (β xt − κ) − Φ∞ (4xt − g)
(11)
(12)
the transitory component for any given variable is given here. The advantage of the approach: the transitory component of given variables can be decomposed into the contributions of individual cointegraing disequilibria and lagged dynamics,respectively. Special case Φ∞ = 0 static relationship Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Infinite Horizon Error Correction Process infinite horizon the nature of B-N trends and transitory components has the the same structure consider two special case in infinite horizon 0 CASE 1 β xt 6= κ and 4xt = g based on (11)and (12) 0
0
0
β (xt − xˆt ) = −β α∞ β (xt − xˆt )
(13)
0
so we get adding-up constraint β α∞ = −Ir 0 CASE 2 β xt = kappa and 4xt 6= g based on (11)and (12) 0
0
0
β (xt − xˆt ) = −β Φ∞ β (4xt − g)
(14)
0
so we get adding-up constraint β Φ∞ = 0n×r Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Example:Bivariate Cointegration VAR(1) · ¸ · ¸ ¤ α1 £ ε 1 −1 xt−1 + 1t 4xt = αβ xt−1 + εt = α2 ε2t 0
(15)
the implied process for single conintegrating relation 0
0
β xt =
β εt 1 − θL
(16)
the two underlying matrices
Φ∞ = 0 · 0
−1
α∞ = −α(β α)
=
Anthony Garratt, Donald Robertson, Stephen Wright
α1 ¸ α2 −α1 α2 α2 −α1
(17) · ¸ −(1 − ξ) = ξ
(18)
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Example:Bivariate Cointegration VAR(1) the implied process for the transitory components 0
0
xt − xˆt = −α∞ β xt = −α∞
β εt 1 − θL
(19)
the process for the trends £ ¤ 0 0 4xˆt = (I − α∞ β )εt = β⊥ α ∞⊥ εt = 1 −1 (ξε1t + (1 − ξ)ε2t ) (20) two key insights in B-N trends σ2P σP T
= σ 2 1 [ξ 2 + (1 − ξ)2 s2 + 2ξ(1 − ξ)ρs] 1 = σ 2 1 [ξ − (1 − ξ)s2 + 2( − ξ)ρs] 2
Anthony Garratt, Donald Robertson, Stephen Wright
(21) (22)
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
Valuation Indicators and the US Stock Market
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Object:analysis the role of two indicators in predicting stock return data: Annual dataset for the US nonfinancial corporate sector 1900-2002 Variables:xt = [vt dt kt lt ] Indicators: dividentd yield defined in terms of total cashflow to 0 shareholders ct = dt − vt = β1 xt Tobin’s q qt = (1 − λ)(vt − kt ) + λ(lt − kt )
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
Valuation Indicators and the US Stock Market On both theoretical and empirical grounds,the two indicators and real returns are stationary processes. Case 1: qt appears stationary,sole cointegrating relation β = β1 I I
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the cashflow dividend is the single cointegrating relation vt and dt share a common stochastic trend kt and lt are close to random walk predicting power of cashflow dividend is weak both the rise and fall in the market must be interpreted as permanent shocks
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
Valuation Indicators and the US Stock Market Case 2: qt appears non-stationary,two cointegrating relation β = [β1 β2 ] I
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the strong growth in B-N trends in vt and dt is muted by the steadier growth of kt predicting power of cashflow dividend is stronger than Case 1 both the rise and fall in the market is almost entirely a movement of transitory shocks
Conclusion:If Tobins q is a cointegrating relation, this is bad news for expected returns in the immediate future, but it is good news for return variance over longer horizons. All transitory components are eliminated. More powerful in predicting. Economic fundamental=⇒Assumption Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
A Small Model for UK Economy
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Object: focus on the transitory components ,examine the transitory movements in UK GDP Model and Data: model of Garratt et al.(2003;2004) macroeconomic data 1965Q1-1999Q4 Variables:xt = 0 [p0 t ; et ; r∗ t ; rt ; 4pt ; yt ; pt − p∗ t ; ht − yt ; y ∗ t ; t] all variables are I(1) andestimate a cointegrating VAR(2) model based on theory
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
A Small Model for UK Economy De-Trending: distinct difference in implied trends and transitory components,depending on whether one or two cointegrating relations were imposed For multivariate, a particular problem is the uncertainty both about r(rank ofβ) and for any given rank, the nature of the cointegrating relationships. Based on the benchmark of r = 0, standard deviation of the transitory component increases with r ”black box”
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
A Small Model for UK Economy Cointegrating relations based on theory: I
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based on economic theory, that there are five fundamental relationships that are assumed to result in stationary processes PPP IRP CONV RMB FIP ∼ I(0) the transitory component in UK GDP are overwhelmingly dominated by movements 28 in cointegrating relations Result: follow the figures, two relationships: CONV and the RMB relation, are key; PPP being the only other relationship for output.
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
US Stock Market A Small Model for UK Economy
A Small Model for UK Economy
The nature of transitory fluctuations can not be separated from the nature of the underlying fundamental stationary processes that drive the economy.
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Conclusions
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interpret B-N trends as conditional cointegrating equilibrium values the nature of the permanent and transitory components can be related to the nature of the error correction process theory and econometric evidence both are crucial in clarifying the nature of uncertainty analysis of fundamental stationary processes has distinct advantages over the atheoretical de-trending processes
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
Outline Introduction Theory Empirical Conclusions
Q and A
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lack statistical indicators interpretation of the empirical result others Thank you!
Anthony Garratt, Donald Robertson, Stephen Wright
Permanent vs Transitory Components and Economic Fundamen
