# Chapter 7: Measuring the growth slowdown with simple regression

In section
3-5 we used the GDP deflator to calculate real GDP. We then computed the percentage
change in real GDP for each pair of consecutive years and used the Descriptives
routine to compute the average percentage growth in real GDP. For the period
1930-1996, the average annual change in real GDP was 3.43 percent. In this section,
we look at another way to measure the growth of GDP or any other variable.

7-1
A compound growth formula

Economic growth
is like compound interest. When growth occurs this year, it is on top of the
growth of last year and the year before that, and so forth. In dollar terms,
five percent growth this year is more than five percent last year because last
year’s growth added to the base of this year’s economy. This is the same as
a bank deposit, where the interest earned this year is based on the original
deposit plus whatever interest has been paid into the account over its life.
Therefore, we can write down a growth formula which looks exactly the same as
the formula for compound interest. If Y0 is GDP in the beginning
year, and it grows at the rate g for one year, it becomes Y1:

Y1 =
Y0(1+g).

If it grows a
second year at the rate g, then Y1 becomes Y2:

Y2
= Y1(1+g) = Y0(1+g)(1+g) = Y0(1+g)2.

Generalizing
this formula, in the year t, Yt equals:

Yt
= Y0(1+g)t.

This is the equation
we estimate with simple regression techniques. First, however, we have to
transform it into a linear equation because as it stands, g enters the equation
in a non-linear fashion (g + 1 is raised to the power t).

Take the natural
logarithm of both sides:

ln(Yt
) = ln(Y0(1+g)t) =

lnY0 + ln(1+g)t =

lnY0 + t*ln(1+g).

Let yt
= ln(Yt), b0 = ln Y0, and b1 =
ln(1+g), then our model becomes

yt
= b0 + b1t,

which can easily
be estimated using the variable "year" for t and the constructed variable
ln(Yt) as the dependent variable. The steps in SPSS are as follows:

1. Select
Transform from the menu bar, then choose Compute. . .;
2. In the
Target Variable box type lrgdp;
3. In the
Numeric expression box type ln(rgdp);
4. Click OK;

(Note that this
assumes that you have created real GDP (rgdp) earlier; if not, then you need
to compute it first as (gdp/gdpdef)*100.)

The next step
selects cases. We will examine the growth slowdown which happened in the early
1970s. We will do this in three steps. First, we will estimate growth over
the whole period, 1948 to 1996. Then we will re-estimate in the two distinct
sub-periods, 1948-1972 and 1973-1996.

1. Select
Data from the menu bar, then choose Select Cases . . .;
2. Click the
button for Based on time or case range, then click Range;
3. Type 1948
in the first box and 1996 in the second;
4. Click OK.

Now, run the regression:

1. Select
Statistics from the menu bar, choose Regression, then Linear . . .;
2. Highlight
lrgdp in the variable list and use the arrow to click it into the dependent
variable box;
3. Do the
same for year, putting it into the independent variable box;
4. Click OK.

The estimated equation
is Yt = -55.704 + 0.03238(Year).

Remember that
the coefficient on year (0.03238) is actually ln(1+g), so to get g, the growth
rate, we have to solve:

ln(1+g) = 0.03238,

1+ g = e0.03238,

g = 0.03291.

The average annual
rate of growth of GDP, 1948 to 1996 was 3.29 percent. Now, let’s look at two
sub-periods: 1948-1972, and 1973-1996. You should get

(1948-1972)
Yt = -66.5837 + 0.03793(Year), Þ g = 3.87%

(1973-1996) Yt = -43.6007 + 0.02628(Year), Þ g = 2.67%.

In other words,
GDP growth in the latter period was more than a full percentage point less
than in the earlier period.

A difference
of 1.2% may not seem like much, and in truth, it isn’t if it’s only a year
or two of slower growth. If, however, it persists for 25 years, then it begins
to make a difference. For example, if our GDP growth rate had been 1.2% higher
for the last 25 years, GDP today would be about 35% larger than it is. An
increase of US GDP by that much would result in an increase from about 8 trillion
in 1997 to 10.8 trillion. This is not trivial (\$2,800 billion), particularly
when you consider that the 2,800 billion is only one year’s worth of lost
output and lower incomes. Cumulatively, the effects are much larger in dollar
terms.

7-2
Possible explanations for the growth slowdown

The same pattern
that holds for real GDP is present in virtually every measure of growth, such
as productivity, real wages, real national income, and so on. You may want to
verify this by conducting a similar analysis on those variables. Naturally,
economists are curious to know why this pattern exists. That is, why did economic
growth seem to slowdown in the 1970s, and why hasn’t more rapid growth returned?
Unfortunately, we do not know the answer. There are, however, many possibilities,
some or all of which may be partially or wholly true. Disentangling cause from
effect is extremely difficult here. One point that stands out, however is that
growth slowed in just about every part of the world economy, not just the US.
That means that whatever the explanation is, factors creating slower growth
are not peculiar to the US alone.

There are a host
of possibilities, each of which has believers:

1. Oil: Some
economists and many non-economists believe this. Their arguments are sophisticated
and hinge on complex econometric analysis. The timing of the beginning of
slower growth more or less coincides with the first oil crisis (1973-74),
but when oil prices crashed in the 1980s, rapid growth did not return.
2. Social attitudes:
Conservatives like to blame the breakdown of the family, easy divorce, decay
of the work ethic, drugs, promiscuity, etc. The problem here is that social
changes have also been beneficial for growth; for example, women and blacks
are able to use their talents more productively today. It’s as if we increased
the pool of talent by more than 50%.
3. Lack of savings
and investment: This is one of the strongest arguments, but then, why did
savings and investment rates fall?
4. The change
in the focus of government policies: The breakup of the Keynesian consensus
led to reduced emphasis of government policies on fighting unemployment
and stimulating growth.
5. The breakup
of the Bretton Woods financial agreements: An indirect effect at most; the
end of fixed exchange rates may have contributed to inflation which spurred
the changes in number 4.
6. Technological
reasons: We have lots of new technology, but we don’t know how to use it
yet. We use computers to make fancy fonts and pretty memos, but not so much
to re-organize how we work. In this view, by the 1970s, we had pushed the
technologies introduced in the 1920s-60s about as far as possible.
7. Government:
Take your pick here. Some (conservatives) say there is too much regulation
and government interference in the economy, while others (liberals) say
the government does too little and has neglected its responsibility to build

As you can see,
there are a lot of possibilities. This topic remains one of the most important
issues in economics.

7-3
Sources
Baumol, William,
Sue Anne Batey Blackman, and Edward Wolff, Productivity and American Leadership:
The Longer View.
MIT Press. 1989.

Federal Reserve
Bank of Kansas City, Policies for Long-Run Economic Growth: A Symposium
Sponsored by The Federal Reserve Bank of Kansas City.
FRB, Kansas City.
1992.