The Solow residual is a number describing empirical productivity growth in an economy from year to year and decade to decade. Robert Solow...defined rising productivity as rising output with constant capital and labor input. It is a "residual" because it is the part of growth that is not accounted for by measures of capital accumulation or increased labor input. Increased physical throughput - i.e. environmental resources - is specifically excluded from the calculation; thus some portion of the residual can be ascribed to increased physical throughput...The Solow Residual is procyclical and measures of it are now called the rate of growth of multifactor productivity or total factor productivity, though Solow (1957) did not use these terms.The Balassa-Samuelsen effect also "assumes that mass-produced traded goods have a higher residual than does the services sector". One problem thus far, is that too many incentives for service sector innovation are misaligned. Part of this is due to the fact that the real time scarcity of populations at an aggregate level - especially in terms of what is possible for mutual obligations - has no public accounting at present. Meanwhile: Instead of contributing to output and aggregate wage capacity, some service sector technology gains are mostly utilized to maintain relative output levels, even as these gains accrue to professional income. Indeed, recent tax changes from the Trump administration, exacerbate this income effect.
A more recent contrast with Solow's earlier contributions, highlights the importance of endogenous factors. According to Wikipedia:
...endogenous growth theory holds that economic growth is primarily the result of endogenous and not external forces, Endogenous growth theory holds that investment in human capital, innovation, and knowledge are significant contributors to economic growth.Nevertheless, the endogenous factor of (formal) human capital investment and its associated risk, includes an asymmetric relationship to overall growth potential, depending on sector. In particular, positive spillover effects have proven more likely in tradable sectors, where innovation often contributes to extensive revenue potential via additional output. In other words, when goods are involved, there's more revenue gain from human capital investment to spread around.
On the other hand, innovations in knowledge application which accrue to the time use scarcities of professional income, are more closely held. After all, time product scarcity means less aggregate revenue, in relation to the human capital investment presently required. This has proven especially problematic, since areas involving high skill knowledge product, tend to be the most prominent areas where taxpayers have contributed to the costs which directly involve human capital.
We can see the effects of these realities, by the fact that overall output gains are held back to a greater extent, than was the case when tradable sectors still commanded a larger presence in advanced economies. Again, consider an earlier defining aspect of the Solow residual which was quite obvious in the fifties: "...rising productivity as rising output with constant capital and labor input." Given non tradable sector dominance - particularly that which is time product related - aggregate output is being held as a relative constant, while more of today's capital is labeled as "intangible", even as labour input is slowly being withdrawn in relation to technology.
Could time arbitrage recapture some of the earlier benefits of the Solow Residual? I believe time arbitrage would be more effective for the preservation and use of knowledge, than taxpayer support for the time based product of today's non tradable service sector activity. Time arbitrage would make it possible to share important facets of knowledge more widely, in a simultaneous framework of symmetric coordination and wealth creation. Equally important, a formal adoption of time arbitrage could reduce the present intangible capital which essentially translates into more services input for knowledge production, than is actually necessary for aggregate output in many instances.
Consider why it is important to get past the confusion of intangible capital. Since human capital investment contributed to output gains for centuries, particularly via tradable sector output, it's easy to assume that formal education as an investment process, "should" lead to similar productivity gains for time based product as well. But time based product is scarce, so when formal education accrues to time based product, one quickly runs into the reality of greater inputs and overall resource capacity, in relation to the outputs that can be derived. This detraction from aggregate productivity, frequently described as intangible capital, is precisely where high skill time based product presents the most problems, for the efficacy of the Solow Residual at the level of aggregate resource capacity.
Apprenticeship provided important ways to address educational aspects of input in relation to output, for time coordination in the past. However, many aspects of the digital era have changed the nature of "learning by doing" - especially since scaling up has ceased to be the desired outcome in many instances. Hence time arbitrage would approach learning by doing as a continuous chain of knowledge application, and adaptation to what have become quickly evolving circumstance.
Perhaps this post wouldn't be complete, without noting the ongoing significance of the Solow Residual in both microeconomic and macroeconomic contexts. For instance, formal educational considerations for worker productivity are often discussed in microeconomic terms, such as in a recent post from Bryan Caplan. Nevertheless, it's the macroeconomic effects of the Solow Residual which hold the most importance, given educational considerations and their potential to either contribute to - or detract from - the nature of economic prosperity.