An econometric-based analysis of the ROI on NASA is presented here:
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The 14 dollar estimate is the cumulative effect on GNP as a result of increasing (and sustaining) the spending on NASA's R&D department, about a decade after the initial increase.
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Be aware that this is from several decades ago.
The source for the 7 dollar estimate seems to be Scott Hubbard, an ex-employee at NASA:
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