Industry & State Level Value Added and Productivity

Industry & State Level Value Added and ProductivityDecompositions

Shipei Zeng1, Stephanie Parsons1,3, W. Erwin Diewert1,2, and Kevin J.Fox1

1School of Economics, UNSW Sydney2Vancouver School of Economics, University of British Columbia

3Reserve Bank of Australia

November 29, 2018

Shipei Zeng & Stephanie Parsons Value added decomposition November 29, 2018 1 / 33

Identifying changes in value added

Value added decomposition

I Parametric and non-parametric estimation of production frontiers

I A recent decomposition proposed by Diewert and Fox (2017)• Free Disposal Hull (FDH) and index number theory• Rule out technical regress• A non-parametric approach involving only observable data


Identifying changes in value added

Value added decomposition

I Value added decomposition for Australian market sector industries• 12 selected industries and 16 market sector industries• Decomposition at an aggregate level and an industry level• Sectoral explanations for Australian TFP change

I Simple enough to be implemented by national statistical offices• Data cubes from Australian Bureau of Statistics• R package: dfvad


Methodology

Defining the optimal output value

I Cost constrained value added function

Rt(p,w , x) = maxy ,z{p · y : (y , z) ∈ S t ;w · z 6 w · x}

I Unit cost function

ct(w , p) = mins

{w · x s

p · y s: s = 1, · · · , t

}


Methodology

Defining the optimal output value

I Rewrite the cost constrained value added function

Rt(p,w , x) = maxs

{p · y s w · x

w · x s: s = 1, · · · , t

}=

w · xct(w , p)

I A sequential approach which rules out technical regress


Methodology

Explanatory factors

I Net output price indexes

α(pt−1, pt ,w , x , s) =Rs(pt ,w , x)

Rs(pt−1,w , x)

I Input quantity indexes

β(x t−1, x t ,w) =w · x t

w · x t−1


Methodology

Explanatory factors

I Input mix indexes

γ(w t−1,w t , p, x , s) =Rs(p,w t , x)

Rs(p,w t−1, x)

I Returns to scale

δ(x t−1, x t , p,w , s) =Rs(p,w , x t)/Rs(p,w , x t−1)

w · x t/w · x t−1

= 1


Methodology

Explanatory factors

I Growth in value added efficiency

et =pt · y t

Rt(pt ,w t , x t)6 1

εt =et

et−1

I Technical progress

τ(t − 1, t, p,w , x) =Rt(p,w , x)

Rt−1(p,w , x)


Methodology

Straightforward decomposition

I Value added growth decomposition

pt · y t

pt−1 · y t−1= αt · βt · γt · εt · τ t

I TFP growth decomposition

TFPG t =pt · y t/pt−1 · y t−1

αt · βt

= γt · εt · τ t


Methodology

A weighted average industry approach

I Tornqvist explanatory factors: λ ∈ {α, β, γ, ε, τ}

lnλt• =K∑

k=1

1

2(skt + sk,t−1) lnλkt

I Approximation of value relatives

ln

(v t

v t−1

)≈

K∑k=1

1

2

(skt + sk,t−1

)ln

(vkt

vk,t−1

)

=K∑

k=1

1

2

(skt + sk,t−1

)ln(αktβktγktεktτkt

)= lnαt• + lnβt• + ln γt• + ln εt• + ln τ t•


Methodology

Establishing a benchmark

I t = 1A1 = 1,B1 = 1,C 1 = 1,E 1 = 1,T 1 = 1

I t > 1

At = αtAt−1,Bt = βtBt−1,C t = γtC t−1

E t = εtE t−1,T t = τ tT t−1

I Level value of productivity

TFPt =pt · y t

p1 · y1 · At · Bt

= C tE tT t


Data

Australian market sector

I 16 industries with productivity data available 1994/95-2016/17(July-June years)

I 12 industries with productivity data available 1989/90-2016/17(July-June years)

I Concerns about measurement problems and research periods


Data

Australian market sector

Table 1: Industry classification of the market sector in Australia

Division Industry

A Agriculture, Forestry and FishingB MiningC ManufacturingD Electricity, Gas, Water and Waste ServicesE ConstructionF Wholesale TradeG Retail TradeH Accommodation and Food ServicesI Transport, Postal and WarehousingJ Information, Media and TelecommunicationsK Financial and Insurance ServicesL Rental, Hiring and Real Estate ServicesM Professional, Scientific and Technical ServicesN Administrative and Support ServicesR Arts and Recreation ServicesS Other Services


Industry-level decomposition

Productivity of 12 selected industries

0.00

0.05

0.10

0.15

0.20

0.25

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Lo

g I

nd

ex

ABS (12)

DF Method with ABS Aggregates

Weighted Industry Aggregation Method



DF Method with ABS aggregates

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Lo

g I

nd

ex

lnT

lnE

lnC

lnTFP



Weighted industry aggregation method

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Lo

g I

nd

ex

lnT

lnE

lnC

lnTFP



Divisions A–D

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Agriculture

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Mining

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Manufacturing

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Utilities

lnTFP lnT lnE lnC



Divisions E–H

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Construction

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Wholesale

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Retail

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Accommodation

lnTFP lnT lnE lnC



Divisions I–K, R

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Transport

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Information

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Financial

−0.4

0.0

0.4

0.8

1990 2000 2010Year

Log

Inde

x

Arts

lnTFP lnT lnE lnC



Thoughts on the industry results

I Only 4 industries showed considerable technical progress beyond 2004• Agriculture, forestry and fishing• Retail trade• Wholesale trade• Financial and insurance services

I Some industries showed little technical progress even earlier than the2004 peak

• Mining (1996)• Electricity, gas, water and waste services (1998)• Information, media and telecommunications (1999)• Arts and recreation services (1991)




I The amount of inefficiency for some industries was huge• Manufacturing• Mining• Electricity, gas, water and waste services• Accommodation and food services• Arts and recreation services

I Some of this inefficiency is probably real and some of it probablyindicates mismeasurement of inputs and outputs



Industry contribution: value added shares

0.00

0.25

0.50

0.75

1.00

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016Year

Sha

re

AgricultureMiningManufacturingUtilitiesConstructionWholesaleRetailAccommodationTransportInformationFinancialArts



Industry contribution: aggregation

I The weighted average industry approach

lnλt• =∑k

1


I From growth value to level value

ln Λt• =∑t

∑k

1


=∑k

∑t

1


=∑k

ln Λkt



Industry contribution: productivity

−0.05

0.00

0.05

0.10

0.15

0.20

0.25

1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017Year

Log

Inde

x

lnTFP_WI

Contributions from:AgricultureMiningManufacturingUtilitiesConstructionWholesaleRetailAccommodationTransportInformationFinancialArts



Industry contribution: efficiency

−0.12

−0.10

−0.08

−0.06

−0.04

−0.02

0.00

1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017Year

Log

Inde

x

lnE




Industry contribution: technical progress

0.0

0.1

0.2

0.3

1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017Year

Log

Inde

x

lnT





I Industry performance contributes to the aggregate level according tovalue added shares

I Efficiency• Unweighted: electricity, gas, water and waste services• Weighted: mining

I Technical progress• Unweighted: agriculture, forestry and fishing• Weighted: financial and insurance services


State-level decomposition

State-level data

I ABS published the first (experimental) estimates of state TFP inJanuary 2018 for 1994/95 to 2016/17

I Data cover 12 selected industries (aggregate only)

I Less-populated states more prone to measurement error and volatility



State-level TFP growth

Average TFP Growth by State, 1994/95-2016/17



Non-mining states

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NSW

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

VIC

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

TAS

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

ACT

lnTFP lnT lnE lnC



Mining states

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

QLD

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

WA

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

SA

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NT

lnTFP lnT lnE lnC




−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NSW

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

VIC

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

QLD

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

SA

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

WA

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

TAS

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NT

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

ACT

lnTFP lnT lnE lnC


Conclusions

Conclusions

I We have used a new decomposition of industry value added growth,applied to official, publicly available data from the ABS

I The role of inefficiency proved to be very large for many industriesand states

• We think that this result is more reasonable than simply interpretingnegative TFP growth as technological regress

• Industries and states with huge amounts of inefficiency should beinvestigated for possible mismeasurement of the underlying inputs andoutputs

I Our method is easily implementable by national statistical offices andprovides policy-relevant information on growth and productivity


Agriculture, Forestry and Fishing

0.00

0.25

0.50

0.75

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Mining

−0.6

−0.4

−0.2

0.0

0.2

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Manufacturing

−0.10

−0.05

0.00

0.05

0.10

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Electricity, Gas, Water and Waste Services

−0.50

−0.25

0.00

0.25

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Construction

−0.1

0.0

0.1

0.2

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Wholesale Trade

0.0

0.2

0.4

0.6

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Retail Trade

0.0

0.1

0.2

0.3

0.4

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Accommodation and Food Services

−0.10

−0.05

0.00

0.05

0.10

0.15

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Transport, Postal and Warehousing

0.0

0.1

0.2

0.3

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Information, Media and Telecommunications

0.0

0.2

0.4

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Financial and Insurance Services

0.0

0.1

0.2

0.3

0.4

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


Arts and Recreation Services

−0.2

−0.1

0.0

1990 1993 1996 1999 2002 2005 2008 2011 2014 2017Year

Log

Inde

x

lnTFP lnT lnE lnC


New South Wales

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NSW

lnTFP lnT lnE lnC


Victoria

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

VIC

lnTFP lnT lnE lnC


Queensland

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

QLD

lnTFP lnT lnE lnC


South Australia

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

SA

lnTFP lnT lnE lnC


Western Australia

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

WA

lnTFP lnT lnE lnC


Tasmania

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

TAS

lnTFP lnT lnE lnC


Northern Territory

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

NT

lnTFP lnT lnE lnC


Australian Capital Territory

−0.1

0.0

0.1

0.2

1995 2005 2015Year

Log

Inde

x

ACT

lnTFP lnT lnE lnC


Documents

Industry & State Level Value Added and Productivity