Download Industry Level & Aggregate Measures of Productivity w

Industry Level & Aggregate
Measures of Productivity w. Explicit
Treatment of Taxes on Products
By Pirkko Aulin-Ahmavaara and
Perttu Pakarinen
Industry vs Product Aggregation in
Calculation of TFP
• Aggregate TFP = log index of final demand – log
index of primary inputs & imported intermediates.
• Industry TFP = log index of industry gross output
– log index of all intermediate and primary inputs.
• Hulten (1978) showed that Domar-weighted sum
of industry TFPs is measure of shift in aggregate
production possibilities frontier (aggregate TFP).
• Now allow for taxes on intermediates that vary by
industry j and commodity i, denoted by dij.
• Purchaser i’s price pMij = (1 + dij)pMBj.
Effect of Taxes on Products
• Ignoring taxes, economy-level Deliveries
to Final uses = Primary inputs + Imported
intermediates.*
• But with taxes, we have at basic prices:
Deliveries to final uses = Primary Inputs +
(1+dM)Imported Intermediates +
dDomDomestic Intermediates
Deliveries to Final Uses = Sum of industry
VA + Imported Intermediates + Taxes
* Primary inputs = pKK + pLL
Industry-level Productivity:
Three Possible Measures
1. Gross gross output: intermediates
produced and consumed w/in an industry
included in output and intermediate inputs
2. Gross sector output: only the output that
leaves the industry counts
3. Value added
With concept 2, djjMjj term is still needed
even though we’ve netted out Mjj
Economy-level Productivity:
Three Possible Measures
• Have to assume that dij = di  j
• Measures are again: 1. Gross gross;
2. Sectoral gross, which = domestic
production delivered to final uses;
3. Value added, which  GDP at basic
prices and = primary inputs.
• Final uses production = primary inputs +
imported inputs + taxes on products, so in
calculation of TFP diMi term plays role like
an input
Covariance and Reallocation Effects
With gross gross & sectoral gross approaches,
difference between aggregate of industries
and economy level TFP includes:
.
.
.
 i j (tij Mij - ti Mi) = Ninds Cov(tij,Mij)
where ti is ave. of the tij = dijmijMij and a dot
over variable denotes its log-change.
Also have capital and labor reallocation effects
under some approaches
Measures Tested
• Economy-level final demands w. single-deflation
• Economy-level final demands w double-deflation
• Aggregated industry-level value added with
double-deflation
• Economy-level VA with double-deflation.
• Used SIOT, not SUT.
• Used level of detail of 55 industries.
Table 1
Single
Double
deflation
deflation
Dom Final Dom Final
Output
6.2
6.1
Mdom taxes
-0.2
-0.2
MM purch pr
3.3
3.3
Primary
1.2
TFP
2.1
VA
Industry
Level
VA
Economy
Level
4.7
4.0
1.2
1.5
1.5
2.0
3.2
2.5
Törnqvist index
• Törnqvist index is not consistent in
aggregation, so problematical for
aggregation of industry-level productivity.
• Aggregation unavoidable if we want to
model intermediate inputs
Take-home Message
• Even though sector gross output concept
cancels out intra-sector intermediates,
dijMij must be included as if it were an
input in calculating TFP.
• Imported intermediates also need to be
included, along with duties.
• Tax distortions cause allocation inefficiency,
so reduction in inefficiency from a rise in
underutilized products looks like TFP growth.
Questions
• Törnqvist index is undefined if an item is 0
in just one time period; didn’t that happen?
• Can a dij change between time periods?
• Where are trade and transport industries?
• Would the use of Laspeyres indexes allow
you to use SUT and keep 180 industries?
• Why are VA results in table 1 so different?
Suggestions
• Reorganize, shorten, add sub-section titles
and add explanations and eqn names to
improve readability.
• Focus on sectoral gross/final demand
concept and use single deflation at the
economy level. Drop the “gross gross”
concept: it has axiomatic weaknesses.
• To avoid problems caused by Törnqvist’s
inconsistency in aggregation, switch to
Fisher. (Reinsdorf & Yuskavage 2006.)
Suggestions 2
• Törnqvist index is generally the best
approximation to Divisia index theoretical
concept we want to estimate, but a
demonstration that its inconsistency in
aggregation is a worse problem than
people think would be quite interesting.