Lecture Twenty Seven
How Well Do Growth Models Work?
(Economics 100b; Spring
1996)
Professor of Economics J. Bradford DeLong
601 Evans,
University of California at Berkeley
Berkeley, CA 94720
(510) 643-4027
phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net/
April
5, 1996
Administration
Review
Successes
Failures
Administration
Review
The basic growth model can be summarized in the figure
below: work with all variables in "per worker" amounts. Draw the "per unit of
labor power" production function little y = little f of little k. Squash this
production function line down toward the x-axis by, at each point on the
function, multiplying it by the savings rate s. Draw a straight line starting at
(0, 0), corresponding to the "required" rate of investment that will keep the
capital-output ratio constant: enough additional savings and investment to boost
the per-worker capital stock by g%, to provide capital for the n% new workers
coming into the economy, and to replace the annual depreciation of the capital
stock.
And where gross savings and investment are equal to the "required" investment
to keep the capital-output ratio constant, that is the steady state of
this economy: capital per worker tends to gravitate to this point of attraction
k*; output per worker tends to gravitate to its point of attraction y* = f(k*);
it may well take generations for this economy to get to the steady state, but
that is where it is heading.
Our production function is:
Yt
= F(Kt , Et Lt
)a
largely for the sake of convenience: this production
function has (a) diminishing returns to each factor, and (b) constant returns to
scale.
Note that we have "EL", where "E" is the efficiencyof labor
is going to be our measure of the state of technology. As time passes, E will
grow--it is as if one worker can handle two machines as well as two workers
could before, and this is going to be the source of long-run growth in living
standards in this particular model.
You could think of other ways to
think about technological progress rather than assuming that it improves the
efficiency of labor directly--that F stays the same but that each worker
is, over time, more and more valuable. But this is the simplest to work out, and
it doesn't matter much.
Successes
How well does this model work? In some cases very well
indeed. Consider Germany's recovery from the devastation of World War
II:
World War II left Western German in the immediate
aftermath of the war with an output-per-worker level that, in real terms, seemed
to correspond to what output per worker had been back in the 1890s: perhaps 1/3
of output per worke on the eve of World War II.
Yet in the immediate
aftermath of World War II the rate of return on what capital there was was very
high--depreciation was very low--and investment was a high share of national
product. Almost immediately after 1946 the German economy began to grow very
rapidly, closing perhaps 1/20 of the distance back to a pre-WWII growth path in
each year.
And as German production began to approach pre-WWII levels,
German growth began to slow down: so that today it is, and has for a decade
been, no faster than in the United States.
- Higher level than would perhaps have been predicted before WWII.
- Present-day growth rate no faster than suggested by growth of "efficiency"
of labor elsewhere in the world.
- Return on investment now more-or-less back to normal levels.
Or consider U.S. aggregate growth in the aftermath of WWII as well: it
looks very stable: Y grows, K, grows, E and L grow:
The first column is the growth of output per worker; the
second column is the share of that growth that is due to increases in the
capital stock; the third column is the computed growth of E (with
a=0.3).
Biggest shift is what we call the productivity slowdown.
Talk about the productivity slowdown.
But overall picture is of pretty
constant growth supported by a more-or-less stable capital-output ratio and
steady growth in labor efficiency.
Failures
The international distribution of productivity, income
and wealth.
Log scale; output per worker on the left hand side; log of
s/(n+g+d) on the right hand side.
Recall from last time that we
had:
where a, we said, was about 0.3. It seems not
unreasonable to suppose that everyone in the world has "access" to the same
"technology"--in which case a country's Y/L should be directly proportional to
its s/(n+g+d).
That's what the figure above seems to show. Why, then, say
that this is a failure? Because a seems to be too large. Slope = 5 which implies
an a=0.83.
And we also know that in this production function a is the
"share" of output that is attributable, in a MPK sense, to capital.
with a pre-tax real return on investment of 10% per year,
and a capital-output ratio of 3, this equation suggests that a=0.3 is the
right number.
Yet out in the real world capital appears to be
vastly, vastly more productive than the returns people get from investing
suggest.
Ways out:
- reverse causation; demographic transition
- externalities
- there are human capital people
- there are equipment investment people
- there are measurement error people
- there are public infrastructure people
The debate continues.
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