An insight into output gap uncertainty: improving total factor - PDF document

An insight into output gap uncertainty: improving total factor productivity cycle estimates by using capacity utilization C.Planas ( a ) , W.Roeger ( b ) and A.Rossi ( a ) ( a ) European Commission, JRC ( b ) European Commission, ECFIN September 2010

Motivation Relying on the output gap (OG) for counter- cyclical policy can be damaging in case of mis- measurement: • Orphanides (2003, JME) argues that underestimation of OG in real-time is responsible for US high inflation in the 1970s. • Nelson and Nikolov (2003, JEB) reach a similar conclusion for the 70s and 80s UK inflation. Both studies attribute the output gap mis- measurement to an undetected slowdown of potential productivity growth.

Motivation In the production function approach OG = TFP gap + labour gap Objective : improve TFP gap estimation. The largest uncertainty is faced during transition years between business cycle phases. For these years OG estimates frequently switch sign when new information becomes available, e.g. 2000 before the 2002 downturn.

Motivation Trend-cycle decomposition of TFP is difficult in real-time also because of data uncertainty: TFP 2000-2009 vintages (logs) 0.78 0.82 0.76 0.58 0.66 0.59 0.52 0.4 0.41 be dk de 0.79 0.83 0.72 0.62 0.58 0.64 0.52 0.47 0.39 el es fr 1.22 0.74 0.93 0.6 0.85 0.7 0.5 0.46 0.48 ie it lu 0.76 0.79 0.97 0.61 0.54 0.77 0.33 0.43 0.58 85 88 91 94 97 00 03 06 09 85 88 91 94 97 00 03 06 09 85 88 91 94 97 00 03 06 09 nl pt uk

Motivation For instance if we apply HP to estimate the TFP gap, assessing whether in 2000 the gap is above or below potential is impossible: HP real-time estimates of the TFP gap 1.8 2.83 2.74 0 0 0 −1.94 −3.02 −1.47 be dk de 3.62 0.76 1.75 0 0 0 −3.18 −1.25 −1.87 el es fr 4.22 1.82 4.77 0 0 0 −5.58 −2.46 −4.25 ie it lu 3.49 4.28 3.01 0 0 0 −2.2 −3.79 −2.82 94 97 00 03 06 09 94 97 00 03 06 09 94 97 00 03 06 09 nl pt uk Same problem occurs in 2007.

Motivation ⇒ To improve real-time OG estimation, the TFP decomposition needs to be stabilized. Our strategy is to complement TFP with a variable that goes along with the business cycle but is free of revisions, namely capacity utilization . Business Survey Indicator (BSI) 4.62 3.47 5.12 0 0 0 −6.75 −5.37 −6.54 be dk de 2.53 3.17 4.5 0 0 0 −4.77 −6.52 −7.41 el es fr 5.6 5.41 3.82 0 0 0 −3.79 −6.44 −13.93 ie it lu 2.64 3 4.37 0 0 0 −6.31 −5.6 −8.56 85 88 91 94 97 00 03 06 09 85 88 91 94 97 00 03 06 09 85 88 91 94 97 00 03 06 09 nl pt uk

Results 1. For most EU countries, loading CU improves the real-time reliability of TFP gap estimates. 2. Due to a slowdown of TFP growth in EU in the last decade, there is a general tendency to overestimate potential growth of TFP ⇔ underestimate TFP cycle and thus OG. This pattern can be accommodated by specifiying a change-point slope.

A model for TFP and CU Use of CU indicators has been previously suggested (Ruenstler, 2002, Proietti et al. 2007), but so far no model-based rationale has been given. A simple model: Y = ( K E K U K ) 1 − α ( L E L U L ) α E: efficiency; U: utilization. Compatible with the TFP -defining equality Y = TFP K 1 − α L α TFP = ( E K U K ) 1 − α ( E L U L ) α if

A model for TFP and CU Separating persistent and short-term elements: ( E 1 − α L ) × ( U 1 − α E α U α TFP = L ) K K = P × C • Efficiency is not measured ⇒ P is unobserved. • Only aggregate CU is available ( U ), without distinguishing between U K and U L . • As U is built from surveys, we expect a high correlation between U and U K . • We assume a positive correlation between U L and U K : u L = γ u K + ǫ (in logs). Hence: c = (1 − α + α γ ) u + αǫ

A model for TFP and CU Our TFP bivariate decomposition is such that: tfp t = p t + c t 1 u t = µ u + βc t + e ut β = 1 − α (1 − γ ) > 1 with dynamics: ∆ p t = w + µ t − 1 µ t = ρ µ t − 1 + a µt 0 < ρ < 1 2 A cos(2 π/τ ) c t − 1 − A 2 c t − 2 + a ct c t = where a µt and a ct are orthogonal white noises.

Model estimation Performed in the Bayesian context using Program GAP downloadable at eemc.jrc.ec.europa.eu . Prior ( · · · ) and posterior densities of β TFP data vintage 2009 1.5 0.8 1 0.6 1 0.4 0.5 0.5 0.2 0 0 0 0.21 0.87 1.52 2.19 0.51 1.04 1.56 2.1 0.01 0.8 1.59 2.39 be dk de 1.5 1 1 1 0.5 0.5 0.5 0 0 0 0 0.51 1.01 1.53 1.08 1.86 2.64 3.42 0.56 1.3 2.04 2.79 el es fr 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 0.05 0.69 1.34 1.99 0.88 1.34 1.8 2.26 0.29 0.9 1.51 2.13 ie it lu 1 2 1 1.5 0.5 1 0.5 0.5 0 0 0 0.31 0.68 1.05 1.43 0 0.67 1.34 2.01 0.21 0.83 1.45 2.08 nl pt uk

Model validation methodology • To check whether CU can enhance the TFP decomposition, we compare three different approaches: HP on forecast-extended series, the univariate trend plus cycle decomposition, and the bivariate TFP-CU system. • We estimate the model recursively with TFP real-time vintages from 2000 until 2009. • We compare the stability of TFP gap estimates for the years 2000 and 2007. • We summarise the corrections to real-time preliminary estimates in terms of revision variances.

TFP cycle for 2000 ( × 100) 2.22 1.81 1.01 1.2 0.35 0 0.18 −1.12 −1.01 be dk de 1.33 1.51 2.65 0.15 0.61 1.55 −1.03 −0.3 0.45 el es fr 4.48 2.08 6.25 3.24 0.86 2.76 2.01 −0.36 −0.74 ie it lu 4.27 1.31 2.89 1.81 1.2 0.28 −0.48 −0.74 −0.66 00 01 02 03 04 05 06 07 08 09 00 01 02 03 04 05 06 07 08 09 00 01 02 03 04 05 06 07 08 09 nl pt uk — — BSI – – HP · · · Univariate • BSI estimates are more stable than univariate. • BSI estimates are more stable than HP for 9 nine countries, i.e. all but EL, NL and UK. • For DK, DE, ES, IT, LU and PT, HP and BSI return initial estimates of opposite signs. • HP revisions lead to a sign switch.

TFP cycle for 2007 ( × 100) 1.48 1.26 2.72 0.58 0.11 1.03 −0.32 −1.04 −0.66 be dk de 1.29 1.14 0.45 0.29 0.04 −0.11 −0.36 −0.71 −1.36 el es fr 2.58 1.23 3.94 0.11 −0.08 1.64 −2.75 −1.02 −0.66 ie it lu 3.16 2.13 1.46 1.1 0 0.97 −0.96 −1.47 −0.19 07 08 09 07 08 09 07 08 09 nl pt uk — — BSI – – HP · · · Univariate • BSI estimates are more stable than HP and univ. • Like for 2000, general tendency to revise upward. • Potential growth is initially over-estimated, most likely because of the constant drift assumption. • BSI attenuates this pattern as BSI is above average in 2007.

Revisions standard deviation ( × 100) 0.89 1.38 1.61 0.87 1 0.56 0.25 0.37 0.39 be dk de 1.33 1.06 1.52 0.88 0.73 1 0.43 0.4 0.48 el es fr 1.52 2.73 2.49 1.95 0.91 1.95 1.42 1.18 0.31 ie it lu 2.01 1.59 1.48 1.43 1.16 1.02 0.87 0.74 0.57 1 2 3 4 1 2 3 4 1 2 3 4 nl pt uk — — BSI – – HP · · · Univariate • In real-time, over 2000-2009 TFP gap estimates that load BSI are on average more stable than HP and univariate. • EL is the only exception.

Relaxing the constant drift hypothesis Instead of a constant drift + AR(1)-slope we consider the change point model: ∆ p t = µ t − 1 + a pt ∆ µ t = S t a µt p ( S t = 0) = p 0 • S t = 0 ⇒ µ t is constant • S t = 1 ⇒ ∆ µ t = a µt .

Relaxing the constant drift hypothesis TFP cycle for 2007 1.33 1.28 1.01 0.78 0.82 0.17 0.22 0.35 −0.68 be dk de 0.36 0.14 0.9 −0.03 −0.19 0.01 −0.73 −0.21 −0.87 el es fr 1.72 1.49 3.52 0.38 0.88 2.36 −0.95 0.26 1.21 ie it lu 1.58 1.21 0.96 0.32 0.75 0.32 −0.95 0.29 −0.31 07 08 09 07 08 09 07 08 09 nl pt uk — — Change-point slope – – Constant drift • Strong improv for BE, DE, FR, IE, IT, NL, PT. • Over 2000-2008, the change-point improves the real-time reliability for 7 countries, and yields results similar to the constant drift for 3 countries.

Common cycle test common cycle idio cycle log p ( x | M 0 ) log p ( x | M a ) p ( M 0 | x ) BE 124.80 121.64 .96 DK 120.34 112.50 .99 DE 118.62 119.15 .37 EL 121.18 121.70 .37 ES 131.70 131.38 .58 FR 129.30 122.52 .99 IE 95.00 92.13 .94 IT 131.63 123.30 .99 LU 97.43 93.04 .98 NL 135.70 128.91 .99 PT 106.56 108.84 .09 UK 129.74 125.14 .99 Note: results based on the 2009 TFP vintage. M 0 : common cycle model M a : idiosyncratic cycle model; p ( M 0 | x ) tests M 0 against M a .

Change-point test constant drift change-point log p ( x | M 0 ) log p ( x | M 1 ) p ( M 1 | x ) BE 124.80 125.34 .63 DK 120.34 124.79 .99 DE 118.62 126.28 .99 EL 121.18 123.54 .91 ES 131.70 136.16 .99 FR 129.30 137.03 .99 IE 95.00 100.62 .99 IT 131.63 138.84 .99 LU 97.43 104.49 .99 NL 135.70 139.00 .96 PT 106.56 111.37 .99 UK 129.74 138.78 .99 Note: results based on the 2009 TFP vintage. M 0 : common cycle model; M 1 : change-point slope; p ( M 1 | x ) tests M 1 against M 0 .