At the Globe and Mail Report on Business, Ian McGugan discusses Gordon's NBER Working Paper in "A heretic's view of the growth dogma." The Sandwichman responds:
Dear Mr. McGugan,
I was very interested to read your column today about Robert Gordon's NBER Working Paper, "Is U.S. Economic Growth Over?" and downloaded Professor Gordon's paper from the NBER site. Although I would agree with Professor Gordon that the expectations -- based on past experience -- of future growth may be questionable, I must note a critical flaw in his analysis. On page 16 of the paper, Gordon states, "By definition, whenever hours per capita decline, then output per capita must grow more slowly than productivity." The problem with this "definition" is that it is a tautology that conceals the distinction between two potential feedback loops in the ratio between hours per capita and productivity.
Arithmetically, total hours is both the numerator in "hours per capita" and the denominator in "productivity." Output is the numerator in both "productivity" and "output per hour" and thus can be factored out by multiplying both sides of the equation by the reciprocal of output (1/output). So, yes, by definition output per capita MUST grow more slowly than productivity. So what? This is a tautology that obscures more than it explains. By such ultra-Malthusian logic, any increase in productivity, given a stable or growing population, must be a "bad thing" because the increase in output per capita will always be slower!
What Professor Gordon overlooks is that reductions in the hours of work per person can lead to gains in total output when current work-time arrangements are not optimal. Those work-time arrangements can include overwork of some people combined with unemployment and underemployment of others. Such disparities are not well captured in such indicators as "hours per capita", which are averages based on dividing one aggregate by another. Even so, even if large reductions in hours per capita led to massive increases in output per capita, the tautology expressed by Gordon would still be trivially "true". That is, it would be arithmetically correct but irrelevant and misleading for all practical purposes.
A similar confusion between arithmetical results and practical outcomes leads Gordon to prescribe immigration as the panacea to the growth dilemma he purports to uncover. And what could be more logical than a purely arithmetical solution to a purely arithmetical problem? Professor Gordon overlooks the possibility that the number of immigrants that could be productively absorbed by a given economy might be constrained by such other factors as fixed capital investment (including infrastructure), natural resources and social and cultural factors. Treating immigration as "numbers" that can be increased or decreased at will like turning on a water tap is an exercise in academic wool gathering.
Traditionally, economists, including Professor Gordon, have routinely dismissed proposals for work-time reduction as being based on a "lump-of-labor" assumption that allegedly presumes an arithmetical solution to unemployment without considering the practical constraints. They make the perennial claim even where no such fallacious assumption can be demonstrated. It is therefore a delicious irony to see Professor Gordon himself plucking both his "problem" and his "solutions" out of the arid arithmetical void. To be blunt, Professor Gordon here commits precisely the "lump-of-labor fallacy" that he elsewhere glibly (and unjustifiably) accuses others of!
P.S.: In answer to Gordon's question, would I rather have an Ipad or a flush toilet, I would much rather have a flush toilet with the capability of disposing of the "heretical orthodoxy" of pedantic scribblers like Professor Robert J. Gordon.