Appendices to chapter 4: D From gross output to value added

Summary

Framework

Here I present a more formal analysis of bias 4 and bias 5 within a simplified model, and I examine their consequences for measuring industry's contribution to GNP. After that, I put forward a methodology for gauging the extent of divergence between trends in value added and gross output at the sector level, which can be executed for three broad industrial sectors (defence industry, basic industry, and light industry).

In chapter 4, the two biases were defined as distortions arising from the application of incorrect weights to gross output series for purposes of measuring sector GNP (value-added) contributions. Bias 4 is generated by gross output value weights, and bias 5 by value-added weights. Below, a true value added index is shown in equation (7), bias 4 is illustrated in equation (12), and bias 5 in equation (14).

The symbols used are listed as follows. A subscript j refers to the jth sector of industry. A subscript t refers to period t. A superscript asterisk indicates a Laspeyres index number based on period t = 0.

1. α material input per unit gross output

2. D price/cost disturbance

3. δ share of price/cost disturbance in nominal gross output

4. H^* a ‘hybrid’ value-added index

5. L labour input, hours

6. λ labour input per unit gross output

7. M material input, units

8. m material input per unit labour input

9. µ the share of sector 1 in total industry value added

10. n price per unit material input

11. […]