Robert Solow And The Club Of Rome

Robert Solow, Nobel prize winner and economist, is first and foremost known for the growth model he described.

As an active researcher Solow steadily (pun intended) tries to validate his growth theory and he came to an interesting conclusion regarding to the rise of productivity of IT: According to his research, a rise in productivity due to computerization is unobservable.

This story has recently been covered by some magazines, for example here.

On the first look, there are is one obvious problems with measurement of productivity: If an innovator like Netflix, for example, offers video on demand for a comparatively low price and all people would switch from their local video store to Netflix, that would lower the “video rental” part of the GDP. However, since assumably more people are now willing to “rent” a video (due to the lower price) that, in contrast will increase that very part of the GDP. The result maybe: Zero change in spite of an innovation.

However, if you forget about the fallcies of measurement, the problem with the unobservability of productivity increase in the computer age is another one: Productivity is, basically, calculated as “i/o”, “input over output”, whereas “input” describes the “factors of production”, such as labor and capital and output describes the GDP.

So, if there is an economy which continuously grows at 5% while keeping its input fixed, that would translate to an increase of productivity of 5%.

Enter The Club Of Rome. There is a notable publication by The Club Of Rome, called “The Limits to Growth” which outlines a very understandable thesis: If we consume (and therefore, destroy) finite resources, the process of growth cannot be infinite.

There is a basic neoclassical (micro)economic model that reflects that: Marginal costs. At a certain point it becomes more “difficult” (expensive) to produce one more unit of output. Of course, that concept applies to macroeconomics, too: If a developed economy has had growth rates of 5% for ten years, it may be more difficult to add another 5% in the eleventh year than it was in the first year. The only measurement for “difficulty” in our productivity calculation are those “factors of production”. However, a developed economy may be at a point where marginal costs begin to rise exponentially. A rise in output of $x%$ would “usually” require a $y > x%$ rise in input factors, but an economy manages to grow with a $y \geq x%$ increase in inputs. Productivity would not change in the classical way, then. But technological improvements can be seen as dividends which make a rise in output on an upward sloping marginal cost curve more achievable.

The bottom line here is that if you have nothing and invent a wheel, productivity rises dramatically. If you already have that wheel, it is more difficult to invent something with the same impact as a wheel.

A possible solution for making technological improvement more visible would be a (very hypothetical) application of an inflation concept.

Let $P$, $I$ and $O$ be the productivity, the inputs and the output, respectively. Our simplified productivity calculation then is:

$ P_i = \frac{I_i}{O_i} $ for each year $i$.

To take into account, that innovation will become more complicated in highly developed economies, we could imagine a calucation like this:

$ P_1 = \frac{I_1}{O_1} $ for year one

( $ P_2 = \frac{I_1}{O_2} $ )


$ P_{2,t} = \frac{I_{2,t}}{O_2} $ for year two.

where $P_{2,t}$ is the hypothetical productivity for year two.

$I_{2,t}$ is the hypothetical amount of input you would have needed $t$ years before to producte $O_2$ units of output.

Then the tech dividend would be $P_{2,t} - P_2$.

The problem of unobservability is not solved this way, though. If you know what if would have taken to produce more output $t$ years ago, you would likely have added these inputs.

So, this is only a very superficial explaination of why productivity seems to stagnate in spite of technological improvements. The amount of the technical dividend remains unobservable.

Further readings
  • The effect of a higher “innovation” / “growth” rate in least developed countries is known as the Catch-Up effect).
  • The cycles of an economy which is unable to maintain infinite growth may lead to Kondratiev Cylces.