The calculating model and empirical analysis of science & technology productivity and its leading GDP’s fluctuating cycle

Aiming at the shortcomings of studying on Science & Technology productivity that only limited to qualitative analysis in academia for a long time, the author, by applying the control theory, constructs a productivity control system for country and region, which involves various production factors as the input and the contribution made by science & technology to GDP (science & technology GDP for short, the same as below) as the output. Furthermore, based on the control system, science & technology productivity which is completely determined by science & technology GDP, quite similar to kinetic energy form in physics, is testified under the condition that system controller R_t takes some special relation. Therefore, calculating model of science & technology productive forces has been given. Using this model, the author has calculated the science & technology productivities in China and America respectively and also calculated the two nation´s fluctuating cycle concerning how long the science & technology productivity precedes GDP through Grey Relation Analysis Model. Finally, it´s approved that the leading GDP of science & technology productivity has a shorter cycle with the development of science & technology, and America witnesses a shorter cycle than our China does at one time. All those are to be used to verify a fact that science & technology productivity, on an inverse proportion to science & technology level, boosts economic growth.