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 d ij. Purchaser i’s price p M ij = (1 + d ij )p MB j.

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+d M )Imported Intermediates + d Dom Domestic Intermediates Deliveries to Final Uses = Sum of industry VA + Imported Intermediates + Taxes * Primary inputs = p K K + p L L

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, d jj M jj term is still needed even though we’ve netted out M jj

Economy-level Productivity: Three Possible Measures Have to assume that d ij = d i 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 d i M i 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 (  ij M ij   i M i ) = N inds Cov (  ij,M ij ) where  i is ave. of the  ij = d ij m ij M ij 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 deflation Dom Final Double deflation Dom Final VA Industry Level VA Economy Leve l Output M dom taxes   0.2 M M purch pr 3.3 Primary TFP

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, d ij M ij must be included as if it were an input in calcula ting 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 d ij 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.