Download Growth Accounting

Lecture on "Growth Accounting"
Question: What Causes Long Run Growth in the Asian Miracle?
Will it be sustained forever or eventually die out?
Theory:
Empirical Application of Neo-Classical Theory – Growth
Accounting
Answer:
Mixed; and Controversial
Inputs and Outputs: The Production Function Revisited
The central feature of any economy is that economic agents take factor inputs--labor, capital, and raw materials---and convert them into useful products. Not
quite alchemy, but useful nonetheless. We call this relation between factor
inputs and output a production function.
Thus we might write
Y = f (K, L, T).
By taking T out and replacing it with A, we get
Y = A F(K,L),
where Y is output (real GNP), K is the stock of physical capital (plant and
equipment), and L is labor (the number and hours of people working).
The letter A measures what we will call productivity. A higher value of A
means that the same inputs lead to more output, as clear a definition of
productivity as I can think of. [Despite this, the word productivity is used in
many different ways. When you run across it in other contexts, your first order
of business is to find out exactly what it means.] For future reference, we'll refer
to A sometimes as total factor productivity, to distinguish it from, say,
average labor productivity, Y/L.
As we'll see shortly, we owe a lot of the growth in the US economy (and other
economies, too) to increases in A. For now, let's think of things that might
affect A.
(i)
Technological progress: It can be thought of as increases in A:
invention of the diesel engine, the transistor, the microchip, penicillin,
and so on.
(ii)
Human Capital Issues: The skill level of the labor force is another
thing that might be incorporated in A. One of the big differences
between rich and poor countries is that the former have better
educated and more highly skill workers. For this reason, we would not
expect NAFTA (the North American Free Trade Agreement with
Mexico and Canada) to result in American wages falling to the level
of Mexican wages. (I'm afraid Ross Perot was out to lunch on this
one.)
(iii)
Input Prices, such as Oil Crisis. We've seen that an increase in the
price of imported oil may leave us with lower GNP, other things
equal, since a greater fraction of gross output goes to oil, less to
capital and labor (hence less value-added). We can think of this as a
downward movement in A (and, in fact, that's what we see in the
data).
(iv)
Non-human and Non-capital Factors affecting the Productivity,
such as the Weather. A drought or extreme cold snap might lead to
lower output for given inputs. Droughts aren't a big deal in the US
economy, since agriculture is a small part of the economy, but it gives
you the idea that lots of things might affect A.
(v)
The economic and legal environment, such as Law and Order, and
Social Cohesion, might also play a role in aggregate productivity.
Most economists think that competitive markets play an important
role in allocating resources in an efficient manner, and this kind of
thinking is behind many of the changes in the former Soviet Union
and Central Europe. Conversely, corruption and red tape are often
given much of the credit for India's lethargic performance.
Sources of Growth: “Growth Accounting Method”
Productivity is the cornerstone of economic growth. We are richer than our
grandparents and than the average person in the third world primarily because
we are more productive. Productivity also affects our competitive position: the
more productive we are the better we are able to compete on world markets. In
short, productivity is the source of the high standard of living enjoyed by the
developed economies relative to the third world or to the same economies fifty
or one hundred years ago.
This section is dedicated to defining and measuring productivity, and using a
theoretical framework to determine the sources of economic growth. The
fundamental relation in productivity measurement is, again, the production
function:
Y = A F(K,L).
This function says, as we've seen, that we get higher output for three reasons:
because more people are working (higher N), because they have more
equipment to work with (higher K), or because capital and labor are used more
productively (higher A, a catchall category). What I'd like to do is decompose
growth in real output Y into components due to each of these three elements -an exercise that has come to be called growth accounting. If the production
function has the form
Y = A K1/3L2/3,
this decomposition has a particularly simple expression. [Don't ask! The
exponents mean that one third of output is paid to capital in profits,
depreciation, etc., and two-thirds to labor, which is about what we see in the US
and many other countries.] Then growth in aggregate output Y is
dY/Y = dA/A + 0.33 dK/K + 0.67 dL/L, (*) –This is called “Total Differential”.
where dX/X represent the percentage rate of change of variable X over the
period considered (for example one year):
dX/X = (Xt - Xt-1)/Xt-1 .
In practice we know all the terms but A, which we compute as a residual. We
generally do not measure A directly, which adds to its enigmatic character.
We can, with little change, use this to account for growth in output per worker,
Y/N, which is more directly tied to living standards than output. Given the
structure of the production function, this can be written
Y/L = A (K/L)1/3 ,
and growth decomposes into
d(Y/L)/(Y/L)= dA/A + 0.33 d(K/L)/(K/L).
What this says is that output per worker can rise for two reasons: because total
factor productivity A is increasing and because the amount of capital per
worker, K/L, is increasing.
Application of the Growth Accounting Method” to Japan
Following World War II both Germany and Japan suffered massive losses to
their capital stocks (think of Kuwait or Iraq following the Gulf War). In the
process of catching up with the rest of the world, they had very high rates of
capital growth that led to high rates of output growth. In the case of Japan, this
process continued into the 1970s. To see this, let's do the numbers. From a
different dataset (constructed by the OECD) we have
U.S.
Japan
1970 1985 Growth 1970 1985
Real Output (Y) 2083 3103 2.66
620 1253
Capital (K)
8535 13039 2.83
1287 3967
Employment (N) 78.6 104.2 1.88
35.4 45.1
Growth
4.69
7.50
1.61
Employment is measured in millions of workers, real output and capital in billions of 1980
US dollars. Growth rates are average annual percentage rates.
Back to our problem.
In levels (as opposed to growth rates) we see that the US was much richer than
Japan in 1970, in the sense that it had much greater output per worker: 26.5
(thousand 1980 dollars per worker) vs 17.5. Where did this differential come
from?
One difference is that American workers in 1970 had three times more capital
to work with: the ratio of K to N was 108.6 in the US, 36.4 in Japan. If we use
our production function, we find that productivity A was also slightly higher in
the US in 1970: 5.64 vs 5.35. Thus, the major difference between the countries
in 1970 appears to be in the amount of capital: American workers had more
capital and therefore produced more output, on average. Of course, you lose a
lot of information in such aggregate comparisons (comparisons by industry
show Japan more productive in some, the US in others), but it gives you some
idea what's been going on.
By 1985, much of the difference had disappeared. It's obvious from the
numbers that the biggest difference between Japan and the US over the 1970-85
period is in the rate of growth of the capital stock. From the basic growth
accounting equation, labeled (*), we find that for the US the output growth rate
of 2.66 percent per year can be divided into 0.93 percent due to capital and 1.26
percent due to employment growth. That leaves 0.47 percent for productivity
growth. For Japan the numbers are 2.48 for capital, 1.08 for labor, and 1.13 for
productivity. The largest difference between the two countries is in the rate of
capital formation: Japan's capital stock has grown much faster than the US's,
raising its capital-labor ratio K/N from 36.4 in 1970 to 88.0 in 1985. These
numbers are summarized in the following table:
Contributions to
Growth
Factor
United States
Capital
0.93
Employment 1.26
Productivity 0.47
Total
2.66
Japan
2.48
1.08
1.13
4.69
In short, much of what we see in this data is simply the Japanese catching up in
terms of the amount of physical capital available for production. Put somewhat
differently, it tells us that capital formation, as measured by the investment rate,
can be more important than productivity growth. For that reason, the low US
saving rate, esp during the 1980s, might be cause for concern.
Nevertheless, some of the difference in growth rates is associated with pure
productivity. By our measure, Japan enjoyed an advantage of 0.66 percent per
year in productivity growth over the US in the 1970-85 period, and by 1985
enjoyed a slight advantage. This result is to some extent due to the data set I've
used. As always in economics, it's best not to make too much of small
differences in fuzzy data. Most studies now suggest that the major
industrialized countries (the US, Japan, Germany, and so on) have roughly
comparable productivities when measured by the best available methods, with
the US in the lead. This is a major change from the 1950s and 1960s, when
there were still large productivity differences between these countries.
Total Factor Productivity Growth in Asia: The Debates on the Asian
Miracle – Controversial
The issue of how much output growth in particular country is due to total
factor productivity growth versus growth in inputs is particularly important to
understand the Asian Miracle and the recent economic crisis in Asia. In
1995, Krugman popularized the controversial view (originally presented by
Alwyn Young) that the Asian economic "miracle" was not due to total factor
productivity (TFP) growth but rather to intensive use of inputs, i.e. a high
growth rate of capital due to the high rates of investment in Asia and a high rate
of growth of labor inputs given the increased labor participation rates in the
region.
This view was very controversial since it implied that very little TFP growth
had occurred in Asia; if true, it also suggested that the very high rates of Asian
growth were not sustainanle in the long run given the expected fall in the rate of
growth of employment and the expected reduction of investment rates.
Krugman's views were highly debated and criticized; in this regard, read the
articles in The Economist "The miracle of the sausage makers" and "The Asian
Miracle: is it over?"
The economic crisis in Asia in 1997, even if originally triggered by large
currency depreciations, appeared to indirectly confirm Krugman's views on the
weakness of the Asian economic model and and fragility of the Asian Miracle.
To see Krugman's point consider the following comparison. Consider three
countries that have been popular recently with emerging-market investors:
Brazil, Mexico and Singapore. Some relevant statistics (which you should take
with a grain or two of salt) include:
Growth Rate
Brazil Mexico
Singapore
Output(Y)
Population(L)
Capital(K)
3.6
2.4
3.0
4.9
2.7
3.2
8.4
6.4
11.3
Note: Growth rates are annual percentages for the period 1960 to 1990.
Using the Growth Accounting Method, we have:
Growth due to the growth of the capital stock (K):
0.33 x dK/K
Growth due to the growth of employment (L):
0.67 x dL/L
Growth due to the growth of productivity (A):
dA/A = dY/Y - 0.33 x d K/K - 0.67 x d L/L
Therefore, we get:
Brazil
Total GDP growth 3.6
Growth due to capital growth: 0.99 = 0.33 x 3.0
Growth due to labor growth: 1.61 = 0.67 x 2.4
Growth due to productivity growth: 1.00 = 3.6 - 0.99 -1.61
Mexico
Total GDP growth 4.9
Growth due to capital growth: 1.06 = 0.33 x 3.0
Growth due to labor growth: 1.81 = 0.67 x 2.4
Growth due to productivity growth: 2.04 = 4.9 - 1.06 -1.81
Singapore
Total GDP growth 8.4
Growth due to capital growth: 3.73 = 0.33 x 11.3
Growth due to labor growth: 4.29 = 0.67 x 6.4
Growth due to productivity growth: 0.38 = 8.4 - 3.73 - 4.29
Krugman argued that the East Asian growth miracle was due to increased inputs
rather than increased total factor productivity. When looking at the above data,
it appears that Krugman’s view might be right. In fact, Singapore grew much
faster than Mexico and Brazil but almost all of the amazing 8.4% growth in
Singapore was due to the growth of employment and the growth of the capital
stock. Only 0.38 of that 8.4 growth was due to total factor productivity (A)
growth. Conversely, a significant component of the growth rate of Brazil and
Mexico was due to the growth of productivity: 42% of Mexico’s growth and
28% of Brazil’s growth is due to growth of productivity as opposed to only 4%
for Singapore. So Singapore grew much faster but only because it mobilized the
labor force (through much higher labor force participation rates for women and
active immigration policies) and had very large and growing investment rates
that increased the capital stock at a 11.3% yearly rate.
Because of the very slow rate of total factor productivity growth, the rate of
growth of average labor productivity was (Y/L) was actually slightly lower in
Singapore (1.99% = 0.38 + 0.33x(11.3-6.4)) than in Mexico (2.2% = 2.04 +
0.33 x (3.2 - 2.7)). Since labor productivity growth is a better measure of the
growth of the standard of living (since it is a proxy for the rate of growth of percapita income), in spite of the fact that Mexican’s GDP grew much more slowly
than the one in Singapore (4.9% against 8.4%), the growth rate of per capita
income and labor productivity was higher in Mexico. Moreover, since a large
fraction of Singapore’s growth was due to high rates of savings and investment,
part of the high growth rates of output were achieved at the cost of lower
growth rates of consumption (since income is equal to consumption plus
savings).
While Krugman thesis is confirmed by the above data for Singapore (and for
many other East Asian countries as well), the significant investments in
physical capital (both private investment and public infrastructures) and human
capital (highly educated labor force) in that region might lead to significant
growth in total productivity in the future; so, the long-term potential growth of
Singapore and other countries in the region might still be very good.
However, as the ability to maintain high rates of labor and capital growth might
not be feasible in the long-run, the Asian region might be successful in
maintaining high rates of growth of output and consumption only if it will
become more efficient in increasing the productivity of the resources used
instead of just mobilizing these resources at faster rates.
Finally, note that Krugman’s criticism of the Asian Growth Miracle has been
taken quite seriously in Singapore. After denying or minimizing for two years
the problem, the Singaporean authorities have now officially accepted
Krugman’s view and started a policy drive to increase Total Factor Productivity
growth: this is a rare example of an academic paper leading to a major change
in economic policies!
See on this the attached article from the Wall Street Journal ("Singapore Swing:
Krugman was Right", October 23, 1996).For more on this debate see an article
on The Economist and a several readings on Asia from Krugman's Web Site.
My Last Caution
The Growth Accounting is not very robust, being too simplistic for a complex
macro performance of the economy.
First, it is not easy to aggregate and measure the Capital.
Second, there may be econometric problems, such as Co-integration, etc.
Third, the coefficients of inputs may not be that simplistic, particularly over
time.
Fourth, it may take a long time for the impact of a technology to show up as an
actual increase in the overall economy's output. The example is well taken by J.
Greenwood's analysis of the electric motor and the computer. He found that it
takes about 20 years for a new technology to manifest itself as an increase in
the total production of an economy.