Industry Level & Aggregate Measures of Productivity w. Explicit Treatment of Taxes on Products

1. Industry Level & Aggregate Measures of Productivity w. Explicit Treatment of Taxes on Products By Pirkko Aulin-Ahmavaara and Perttu Pakarinen

2. 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.

3. 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

4. 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

5. 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

6. Covariance and Reallocation Effects With gross gross & sectoral gross approaches, difference between aggregate of industries and economy level TFP includes: . . . åi å j (tij Mij-ti Mi)=NindsCov(tij,Mij) whereti 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

7. 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.

8. Table 1

9. 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

10. 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.

11. 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?

12. 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.)

13. 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.