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# Blowing-Up Our Sample to Get an Estimate for Total Manufacturing

In this section we blow up our sample results for 17 industries to arrive at estimates for the manufacturing sector as a whole.

Previous investigators'followed different options in order to blow up their sample for manufacturing as a whole. Rostas (1948), Maddison (1952), Galenson (1955), Frankel (1957), Mensink (1966), and Yukizawa (1978) simply assumed that their sample results were representative for manufacturing as a whole (either explicitly or implicitly). They presented their overall result in terms of labour productivity, not output or PPPs. Sometimes, as with Rostas, and Yukizawa, their aggregate results were derived by using labour weights.

Three other studies explicitly discuss the aggregation problem in all three dimensions (output, PPPs and labour productivity), i.e. Paige and Bombach (1959), the Czech Statistical Office/INSEE (1969) and West (1971). but they each followed different methods.

Paige and Bombach covered about half of output in their two countries, i.e. the UK and the USA, and their average result is very similar to that for their sample, as they predominantly assumed their quantitative relationships to be representative (see p. 102). They got their total for manufacturing by blowing up the industries they covered to represent the situation by major branch (using quantity relationships of their sample in 59 per cent of cases, PPP relatives for 19 per cent, other price information for 10 percent, and employment for 12 per cent).

West did not make estimates by major branch, but assumed the averag6 PPP for his sample (with value added weights) was representative for the non-sampled industries, uising the sample average PPP to derive real output in the non-covered sector (see p. 26). His overall labour productivity result was significantly lower than that for his sample.

The authors of the Czech-French study used an unweighted average of their sample PPPs (by branch) to get a PPP for each branch, with output derived for the branch by applying this PPP to calculate branch value added in real terms. Their manufacturing total was derived by summing the branch totals. A similar procedure was used by Smith, Hitchens and Davies (1982) and Smith (1985).

Our approach comes closest to that of the Czech-French study. We have assumed that the PPPs for our sample were representative for the non-sampled industries in the same manufacturing branch. For reasons already explained above (see p. 34), we feel that the PPP relationships are more representative than the quantitative relationships which Paige and Bombach predominantly used to establish their aggregate result. Unlike the Czech-French study, we used a weighted average of our individual industry PPPs to arrive at the PPP for each branch. For example our PPP for the food manufacturing branch is the weighted average of the price ratios for grain mill, sugar and sugar products. Table 3.14 shows our PPPs for 13 manufacturing branches. In some cases we combined divisions, because PPPs were not available for each division separately (for example for wood products and furniture). These branch PPPs were used to convert branch value added at national prices to a common currency unit (see the qu.antity relatives in tables 3.15 and 3.16).

In tables 3.15 and 3.16 we moved to a national accounts basis which was not possible in our detailed calculations for the sample industries.