integrated industry-level and aggregate tfp-measures: different approaches pirkko aulin-ahmavaara,...
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Integrated industry-level and aggregate TFP-measures: Different approaches
Pirkko Aulin-Ahmavaara, Perttu Pakarinen, Sami Toivola
Statistics Finland October , 2004
Economy as a unit of production
Economy is here treated as a unit of production that consists of sub-units called industries.
The output of an industry
• Gross output at basic prices?
• Gross value added at basic prices?
• “Sectoral” output at basic prices?
Economy as a unit of production
Tthe output of an economy?
• Gross value added at basic prices?
• Deliveries to final demand (of domestic products) at basic prices?
• Gross domestic product at market prices?
• Deliveries to final demand at market prices?
• Net value added at basic prices?
• Etc.
Two different approaches in this paper
• Deliveries to final demand (of domestic products at basic prices) approach
• Value added (at basic prices) approach
Deriving TFP measures from accounting equations
vpzq '' q is the price vector of outputs
z is the vector of output quantities
p is the price vector of inputs v is the vector of input quantities
ii
ij
ij
jjj
iii
pdqd
vdzdtd
loglog
logloglog
Rate of TFP -growth:
yd log is the logarithmic time derivative of y
(1)
(2)
(Jorgenson and Griliches, 1967)
Price concepts
is the basic price received by the producer. Basic price of a product is assumed to be identical in all its uses
jq
jji qp
is the purchaser’s price paid by the user minus any trade and transport margins, which are treated as separate products. Thus
Taxes minus subsidies on products paid by the user
jip
Industry-level
llj
Ll
kkj
Kk
i
Mij
Mi
i
Mij
Mij
i
Mij
Mi
iiji
iijij
iijijj
LpKp
MqMpMq
MqMpMqQq
)(
)(
)]loglog
log)(log
log)(log
log[)(log 1
lijlj
Lljkj
kkj
Kkj
Mij
i
Mij
Mi
Mij
Mij
i
Mij
Mi
iji
ijiijiji
iji
jjjjjj
LdLpKdKp
MdMqpMdMq
MdMqpMdMq
QdQqQqtd
(3)
(4)
Deliveries to final demand approach
.
)()(
ll
Ll
kk
Kk
i
Mi
Mi
Mi
i
Mi
Mi
iiii
j ijij
jjj
jjj
LpKp
MqpMqMqp
MqQqYq
.]loglog
log)(log
log)(log[)(log 1
lll
Llk
kk
Kk
Mi
i
Mi
Mi
Mii
i
Mi
Mi
ii
iiij
jjjj
jj
LdLpKdKp
MdMqpMdMq
MdMqpYdYqYqTd
Economy level, economy as a single unit of production
(7)
(8)
Aggregation from industry level
)]loglog(
)loglog(
)log)(log)((
)log)(log)((
log[)(log 1
lll
Ll
j lijlj
Llj
kk
kKk
jkj
kkj
Kkj
Mi
i
Mi
Mi
Mi
j
Mij
i
Mij
Mi
Mij
ii
iiij
iji
ijiij
jjjjj
jj
LdLpLdLp
KdKpKdKp
MdMqpMdMqp
MdMqpMdMqp
tdQqYqTd
(10)
ZZj pp if for all values of j then
ZdZpdZp
dZpZdZp
ZZ
jj
Zjj
j
Zj
log
log
and the reallocation term disappears
(11)
Deliveries to final demand approach
Value added approach
Industry level
llj
Llj
kkj
Kkj
i
Mij
Mijij
iijjjjj
LpKp
MpMpQqVv
]loglog
log[)(log 1
lijlj
Lljkj
kkj
Kkj
jjjjjvj
LdLpKdKp
VdVvVvtd
Value added
Rate of TFP growth
(12)
(15)
)]loglog
log[()(log 1
ll
lLlk
kk
Kk
jjjjj
jj
v
LdLpKdKp
VdVvVvTd
Economy-level
.
ll
Ll
kk
Kk
j i
Mij
Mij
j iijij
jjj
jjj
LpKp
MpMpQqVvValue added
Rate of TFP growth
(13)
(16)
Value added approach
)]loglog(
)loglog(
log[)(log 1
ll
lLl
jkj
kkj
Kkj
kk
kKk
jkj
kkj
Kkj
j
vjjjj
jj
v
LdLpKdKp
KdKpKdKp
tdVvVvTd
Aggregation from industry level
i
Mi
Mi
Mi
i
Mi
Mi
iiii
jjj
jjj
MqpMqMqp
VvYq
)()(
Obs.
(14)
(20)
Value added approach
Relationship between the measures based on the two approaches
Industry-level
Economy-level
jjjjjvj tdQqVvtd log)()(log 1
)]log)(log)((
)log)(log)((
log)[()(log 1
j
Mij
i
Mij
Mi
Mij
Mi
i
Mi
Mi
Mi
jij
iijiiji
iiii
vj
jjj
jj
MdMqpMdMqp
MdMqpMdMqp
TdVvYqTd
(21)
(19)
Value added approach 2, economy level value added
Price and quantity of economy-level value added
Accounting identity
j
jjj
j VvVvvV
l
lLl
kk
Kk LpKpvV
)loglog
log()(log 1
ll
lLlk
kk
Kk
W
LdLpKdKp
VvVdvVTd
Rate of TFP-growth
(23)
(24)
(25)
)]loglog(
)loglog(
)loglog(
log[)(log 1
j lljlj
Lljl
ll
Ll
jkj
kkj
Kkjk
kk
Kk
jjjj
jjjj
W
LdLpLdLp
KdKpKdKp
VdVvVvVd
tdQqvVTd
Aggregation from industry level
(26)
Value added approach 2, economy level value added
Application based on the Laspeyres indices
It was possible to replicate the system based on the theoretical Divisia indices.
Application based on the Törnqvist indices
The value added approach:
It was possible to have similar formulas for both industry-level and economy level TFP growth as those in the theoretical system.
Also the aggregation rule has the same terms as those in the theoretical case.
Application based on the Törnqvist indices
))log((log(
))log((log(
)log(log
1
1
jjj
k kjkj
jj
jj
jj
jj
jj
j jj
k kk
jjj
l ljlj
j jj
jj
jjj
jj
j jj
l ll
vj
jjj
jj
j
v
KQq
Kp
Vv
Vv
VvK
Vq
Kp
LQq
Lp
Vv
Vv
VvL
Vv
Lp
tVv
VvT
Application based on the Törnqvist indices
But the reallocation terms do not disappear if all the industries pay identical prices for their capital and labour inputs.
They only disappear if rates of growth of labour and capital inputs are identical in all the industries.
Application based on the Törnqvist indices
Let the price p of an input x to be equal to one in both of the years 0 and 1. Furthermore
))/()/)((2/1(1100
jjjjj xxxxw
For the reallocation term to disappear we should have
)ln(lnlnln 0101jjjjj xxwxx
Application based on the Törnqvist indices
Deliveries to final demand approach
The formulas for TFP-growth included the same terms as those in the theoretical system and in the system based on Laspeyres indices.
But additional terms representing the reallocation of industries’ output between intermediate and final uses and the reallocation of intermediate inputs at basic prices between industries were needed in the aggregation equation.
Calculations using data for Finland
Choice 1. SUTs or SIOTs?
We were using SIOTs to keep the formulas somewhat more simple.
Calculations using data for Finland
Choice 2. Is the level of aggregation used in the deflation the same as the one used in the calculation?
Since product baskets can be different in different uses deflation at lower level of aggregation means relaxing the assumption of identical basic prices in different uses.
This again means that in the deliveries to final demand approach terms representing the price differences are not any more only about taxes and subsidies or that additional terms representing the differences in basic prices are needed both in economy level TFP equation and in the aggregation equation.
Calculations using data for Finland
Choice 3. Are the deflators based on basic prices or basic prices plus net taxes on products?
If basic prices then we can assume that the growth rates of the volumes of taxes and subsidies are equal to those of output in respective uses.
If basic prices plus net taxes on products then we assume that the share of net taxes on a product is the same in all of its uses.
But this does not hold in a VAT-system. And also not necessarily for other product taxes since the uses consist of different product baskets.
Results 2001/2000Table 1. Economy level TFP-growth and contributions to the economy level growth of output
Deliveries to final demand approach Value added approachLaspeyres
(29)*Törnqvist 1
(39)*Törnqvist 2
(44)*Laspeyres
(36)*Törnqvist(50*)
Growth of output 0,954 1,036 0,975 1,609 1,528Net taxes on domestic products inintermediate uses**
0,081 0,060 0,060
Imported intermediate inputs -0,322 -0,338 -0,338Net taxes on imported products inintermediate uses
0,008 0,004 0,004
Labour 0,262 0,266 0,266 0,343 0,345Capital 0,721 0,702 0,702 0,942 0,909Economy level TFP growth 0,204 0,342 0,281 0,325 0,274
Results 2001/2000Table 2. Contributions to the economy level TFP growth
Deliveries to final demand approach Value added approachLaspeyres
(32)*Törnqvist 1
(42)*Törnqvist 2
(45)*Laspeyres
(37)*Törnqvist
(51)*Industry level TFP growth -0,270 -0,196 -0,196 -0,353 -0,263Reallocation of- Industry output between final andintermediate uses
0,061
- Intermediate uses of domesticproducts
0,116 0,116
- Net taxes on domestic products inintermediate uses**
-0,037 -0,031 -0,031
- Intermediate uses of importedproducts
-0,009 -0,009
- Net taxes on imported productsintermediate uses
-0,007 -0,012 -0,012
- Labour 0,224 0,215 0,215 0,292 0,280- Capital 0,295 0,198 0,198 0,386 0,259Economy level rate of TFP growth 0,204 0,342 0,281 0,325 0,275
Results 2000/1999
Contribution to the economy level growth of outputDeliveries to final demand approach Value added approachLaspeyres Törnqvist 1 Törnqvist 2 Laspeyres
Growth of output 8,456 8,175 8,298 5,336Net taxes on domestic products in intermediate uses -0,171 -0,221 -0,221Imported intermediate inputs 4,215 4,030 4,030Net taxes on imported products in intermadiate uses 0,090 0,100 0,100Labour 0,672 0,648 0,648 0,843Capital 0,474 0,471 0,471 0,595Economy level TFP growth 3,176 3,149 3,272 3,897
3,176 3,149 3,269 3,897
Results 2000/1999Contributions to the economy level TFP growth
Deliveries to final demand approach Value added approachLaspeyres Törnqvist 1 Törnqvist 2 Laspeyres
Industry level TFP growth 2,273 2,860 2,860 2,854Reallocation of Industry output between final and intermediate uses -0,123Intermediate uses of domestic products -0,930 -0,930Net taxes on domestic products in intermediate uses 0,013 0,001 0,001Intermediate uses of imported products 0,320 0,320Net taxes on imported products intermediate uses 0,059 0,101 0,101Labour 0,298 0,276 0,276 0,374Capital 0,534 0,645 0,645 0,670Economy level rate of TFP growth 3,176 3,149 3,272 3,897