Measuring the Contributions of
Productivity and the Terms of Trade
to Australian Economic Welfare
OECD Workshop on Productivity Analysis
and Measurement; Bern October 17, 2006
Erwin Diewert and Denis Lawrence
Introduction

We ask two questions:

Have changes in Australia’s Terms of Trade improved economic
welfare?

What is the ‘right’ measure of economic welfare to look at?

To answer the first question, we use the framework in Diewert and
Morrison, Economic Journal 1986

To answer the second question, we suggest using a net real
income measure
Terms of Trade Problem

Market sector GDP function:
gt(P,x)  max y {Py : (y,x) belongs to St}

Value of outputs equals value of inputs in period t:
gt(Pt,xt) = Ptyt = Wtxt ; yt is output; xt is input;


Real income generated by market sector in period t is
t  Wtxt/PCt = wtxt = gt(pt, xt) = Ptyt/PCt = ptyt
where PCt is consumption price
This is the amount of consumption period t income can buy
and this will be our suggested economic welfare measure.
Identifying the
Contributions


The main determinants of growth in real income generated by the
market sector of the economy are:
 Technical progress or improvements in Total Factor
Productivity;
 Growth in domestic output prices or the prices of
internationally traded goods and services relative to the price
of consumption; and
 Growth in primary inputs.
We need a way of identifying the effect of each of these factors in
isolation, ie what would have happened to real income if only
each of these changes had occurred separately and all else
remained the same?
Productivity Growth

Definition of a family of period t productivity growth factors:
(p,x,t)  gt(p,x)/gt-1(p,x)


Laspeyres type measure: Lt
(pt-1,xt-1,t)  gt(pt-1,xt-1)/gt-1(pt-1,xt-1)

Paasche type measure:
Pt

Fisher type measure:
t

But how can we empirically implement the above theoretical
definitions? It can be done by assuming a translog technology.
 (pt,xt,t)  gt(pt,xt)/gt-1(pt,xt)
 [Lt Pt]1/2
Real Output Price
Growth Factors

Definition of a family of period t real output price growth factors:
(pt-1,pt,x,s)  gs(pt,x)/gs(pt-1,x)

Laspeyres type measure: Lt

(pt-1,pt,xt-1,t-1)
 gt-1(pt,xt-1)/gt-1(pt-1,xt-1).
Pt

(pt-1,pt,xt,t)  gt(pt,xt)/gt(pt-1,xt).

Paasche type measure:

Fisher type measure:

Gives increase in real income due to changes in real output prices
t
 [Lt Pt]1/2
Input Quantity Growth
Factors

Definition of a family of period t input quantity growth factors:
(xt-1,xt,p,s)  gs(p,xt)/gs(p,xt-1)

Laspeyres type measure: Lt

(xt-1,xt,pt-1,t-1)
 gt-1(pt-1,xt)/gt-1(pt-1,xt-1).
Pt

(xt-1,xt,pt,t)  gt(pt,xt)/gt(pt,xt-1).

Paasche type measure:

Fisher type measure:

Gives the increase in real income due to input growth alone
t
 [Lt Pt]1/2
Real Income Growth
Decomposition




The input growth and real output price contribution factors (to
real income growth) can be broken down into separate effects that
are defined in similar ways.
With the assumption of a translog technology, we can get the
following exact decomposition of real income growth into
contribution factors:
t/t-1  t = t t t where t = wtxt/ wt-1xt-1 is observable and
ln t = ln PT(pt-1,pt,yt-1,yt) and ln t = ln QT(wt-1,wt,xt-1,xt);
where PT is the Törnqvist (real) output price index and QT is the
Törnqvist input quantity index.
We cumulate the now observable relationships t/t-1 = t t t
into the “levels” relationships t/t-1 = Tt At Bt
Terms of Trade
Contribution Factors





The terms of trade contribution factors are made up of two
separate effects (which we combine in the following figures):
A real export price effect which adds to real income growth if the
price of exports increases more rapidly than the price of
consumption and
A real import price effect which adds to real income growth if the
price of imports falls compared to the price of consumption
In the present setup, the entire value of investment is converted
into consumption equivalents and added to actual consumption
and the price of capital is the usual user cost of capital which
includes a depreciation term.
But this framework overstates real (sustainable) consumption by
the amount of depreciation
The Real Net Income
Approach




In the final part of the paper, we take depreciation out of user cost
and instead subtract it from gross investment.
Now investment is converted to consumption equivalents only if it
is positive after netting out depreciation; thus, we have moved
from real GDP (GDP deflated by the consumption price index) to
real NDP (NDP deflated by the consumption price index).
The remaining user cost term is the reward for waiting or
postponing consumption; thus, income is now labour income
plus the net return to capital.
In the net framework, the role of TFP growth is magnified and in
the Australian data, the role of capital deepening is diminished as
we shall see.
Diewert-Lawrence
Database







Initially developed for DCITA
Extended market sector coverage – covers 16 of the 17 sectors in
the National Accounts instead of the ABS MFP’s 12 sectors
Builds up an output measure from final consumption components
rather than sectoral gross value added
Outputs and inputs are measured in terms of producer prices
rather than consumer prices
Constructs consistent capital and inventory input series and
measures inventory change in a consistent manner
Runs from 1959-60 to 2003-04
This version includes a balancing real rate of return and improved
capital tax treatment
7
5
Imports
2004
9
2002
10
2000
11
1998
12
1996
1994
1992
4
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
Price Indexes
14
13
Government
Consumption
8
Investment
6
Exports
3
2
1
0
2004
2002
6
2000
22
1998
4
1996
10
1994
12
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
Price Indexes (cont’d)
26
24
Labour
20
18
16
14
Domestic
Output
8
Capital
GDP
2
0
Individual Contributors
to Real Income - GDP
2.0
Productivity
1.8
Labour
Input
1.6
Capital
Input
1.4
1.2
Terms of
Trade
1.0
Domestic Output
Price
0.8
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0.6
Cumulative Contributions
to Real Income - GDP
6
Dom. Output Price
Dom. Output Price + ToT
5
Dom. Output Price + ToT + Capital Input
4
Dom. Output Price + ToT + Capital Input + Labour
Input
Dom. Output Price + ToT + Capital Input + Labour
Input + Productivity = Real Income
3
2
1
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0
Investment Price
Indexes
13
12
11
Waiting Capital Services
10
9
8
Gross Investment
7
Depreciation
6
Net Investment
5
4
3
2
1
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0
Investment Quantities
30,000
$1960m
Gross Investment
25,000
20,000
Net
Investment
15,000
Waiting Capital Services
10,000
5,000
Depreciation
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0
Individual Contributors
to Real Income - NDP
2.2
Productivity
2.0
1.8
Labour
Input
1.6
1.4
Capital
Input
1.2
Terms of Trade
1.0
Domestic Output Price
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0.8
Cumulative Contributions
to Real Income - NDP
6
Dom. Output Price
Dom. Output Price + ToT
5
Dom. Output Price + ToT + Capital Input
4
Dom. Output Price + ToT + Capital Input + Labour
Input
Dom. Output Price + ToT + Capital Input + Labour
Input + Productivity = Real Income
3
2
1
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0
2003
2001
2.0
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
Alternative TFP Indexes
2.4
2.2
D-L NDP
1.8
1.6
D-L GDP
1.4
ABS
1.2
1.0
0.8
0.6
Individual Contributors
to Real Income - NDP
1.3
Productivity
1.2
Labour Input
1.1
Terms of Trade
Capital Input
1.0
Domestic Output Price
0.9
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Cumulative Contributions
to Real Income - NDP
1.6
Dom. Output Price
1.5
Dom. Output Price + ToT
Dom. Output Price + ToT + Capital Input
1.4
1.3
Dom. Output Price + ToT + Capital Input + Labour
Input
Dom. Output Price + ToT + Capital Input + Labour
Input + Productivity = Real Income
1.2
1.1
1.0
0.9
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Conclusions



For Australia, we find that changes in the terms of trade, while
important over a few short periods (including recent years), are
not a long run explanation for the improvement in Australian
living standards over the period 1960–2004.
When we move to a net domestic product framework from a gross
domestic market sector framework, the role of capital deepening
as an explanatory factor for improving living standards is reduced
and the role of technical progress (or TFP growth) and labour
growth is increased.
The results emphasise the importance of maintaining a vigorous
productivity reform program – favourable movements in
commodities prices over short periods cannot be relied upon to
sustain ongoing improvements in Australia’s living standards.