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 is the price vector of outputs is the vector of output quantities is the price vector of inputs is the vector of input quantities Rate of TFP -growth: 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 is the purchasers 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

Industry-level (3) (4)

Deliveries to final demand approach Economy level, economy as a single unit of production (7) (8)

Aggregation from industry level (10) if for all values ofthen and the reallocation term disappears (11) Deliveries to final demand approach

Value added approach Industry level Value added Rate of TFP growth (12) (15)

Economy-level Value added Rate of TFP growth (13) (16) Value added approach

Aggregation from industry level Obs. (14) (20) Value added approach

Relationship between the measures based on the two approaches Industry-level Economy-level (21) (19)

Value added approach 2, economy level value added Price and quantity of economy-level value added Accounting identity Rate of TFP-growth (23) (24) (25)

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

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 For the reallocation term to disappear we should have

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 2001/2000

Results 2000/1999