We develop a theory for the amplification of technological improvement by the production network structure of the economy and test it against data. Improvements in a given industry are passed on to all industries for which it is an input. To the extent that industries form a chain, improvements are passed down the chain and accumulate multiplicatively. Using a simple model for technological improvement we show how local improvements are amplified within an arbitrary network structure, and how these can be inferred empirically from industry price indices. We introduce a generalized output multiplier that quantifies this amplification and show that at the level of the whole economy it is invariant under aggregation. Making the bold assumption that all industries in all countries improve at the same rate leads to testable predictions about industry price indices and their variance, as well as GDP growth and its variance. We analyze data for 40 countries and 35 industries from 1995 to 2009 from the World Input-Output Database and demonstrate that the output multipliers are strongly correlated to economic growth. A regression of GDP growth of countries against their output multipliers has an R2 equal to 0.40, and when other standard explana- tory variables for economic growth are added to the regression, the output multiplier remains the most significant variable.