Multi-factor productivity based on output

It is justified to assume that there is exchange of intermediate products between industries. For instance, industry x may supply conductors for industry y. The conductors of industry x are the final products of industry x, but not the end products for the whole production chain. Industry y utilises conductors for manufacturing its own end products, e.g. this is the case in industries that produce technical devices or other high tech equipment. When using the value added method, the contribution of the intermediate input remains unnoticed. Output based productivity calculation accounts for this effect:
The calculation formula for multifactor productivity changes into form: ?multifactor productivity?_output=change in output-(contribution of capital +contribution of labour + contribution of intermediate consumption)