Computers and Productivity musings

[enilsson@xxxxxxxxx]

The 'true' impact of growth rate of the computer sector on the growth rate of
the whole economy is impossible to measure.

The reason has to do with how real series (real GDP, real compensation, etc)
are generated.

Suppose you have 2 sectors in the economy: computers and food. Suppose you
select 1990 as your ?base year.? Among other things, this means that you
determine the ?size? of the two sectors according to the relative spending on
the two items. Suppose that in 1990, then, 10 percent of spending went to
computers and 90 percent went to food. The computer sector is 10% of the
economy while food is 90% of the economy.

The growth rate of the economy would then be 10% times Cg plus 90% times Fg,
where Cg and Fg are the growth rates in computers and food.

Let?s say that nominal spending remains the same in the two sectors between
1990 and 2000. (BEA data seems to suggest that nominal spending on computers
was fairly constant between these years, but this seems odd to me).

Suppose also that productivity/quality advances in computer is such that
the ?true? size of the computer sector is now 50% of the economy and food has
fallen to 50%.

The new productivity rate for the whole economy is now: 50% times Cg plus 50%
times Fg. The computer sector?s higher growth rate now plays a greater role in
boosting the growth rate of the whole economy.

Putting hypothetical numbers into the above:

Suppose the computer sector productivity is always 10% and that in food is
always 2%

In 1990 the economy-wide productivity will be:
10% times 10% plus 90% times 2% = 2.8%

But in 2000 the growth rate of the whole economy will be larger because the
computer sector has grown in importance and its growth rate is now weighted
more:

In 2000 the economy-wide productivity will be:
50% times 10% plus 50% times 2% = 6.0%.

That is, the growth rate has sped up not because any individual industry become
more productivity but simply because the more productivity industry grew in
relative importance.

Now let?s say that we decide to use 2000 as the base year. Because nominal
spending on computers and on food in 2000 is the same as in 1990 (I assumed
this above), the weights for the two sectors is now: computer = 10% and food =
90%.

The new economy-wide growth rate is, then:
10% times 10% plus 90% times 2% = 2.8%.

The growth rate has fallen back to 1990 levels because the 2000 and 1990
spending levels were the same! It seems the computer industry just ain't as
important as it once was when 1990 was used as the base year.

This example shows that the impact of the computer industry on economy-wide
productivity spends on the base year chosen. Those close to today the base year
is, the smaller the role computer productivity has on the economy-wide level fo
productivity.

Conclusion: take with a grain of salt any estimate of economy-wide productivity
growth. Such a number depends on the nominal spending within the different
sectors in the base year chosen.

Similar sort of things happen with the construction of price indexes and in the
construction of most any real series with more than a single component.

Eric