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Was the role of technological progress formalised by Solow (1956) for the first time? or at least he provided the initial formal insight into the role of technological progress in economic growth?

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The Solow model was indeed the first model to account for technological progress.

While models like the the Harrod-Domar model and the Neo-Marxian Feldman–Mahalanobis model conciser investment and saving as contributors to economic growth, they don't consider any measure of technology like total factor productivity to contribute to economic growth, like the Solow Residual.

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