*1998; Last Modified 14 August 1998*

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.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 Y_{0}is GDP in the beginning

year, and it grows at the rate g for one year, it becomes Y_{1}:

Y_{1 }=

Y_{0}(1+g).If it grows a

second year at the rate g, then Y_{1}becomes Y_{2}:

Y_{2}

= Y_{1}(1+g) = Y_{0}(1+g)(1+g) = Y_{0}(1+g)^{2}.Generalizing

this formula, in the year t, Y_{t}equals:

Y_{t}

= Y_{0}(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(Y_{t}

) = ln(Y_{0}(1+g)^{t}) =lnY

_{0}+ ln(1+g)^{t}=

lnY_{0}+ t*ln(1+g).Let y

_{t}

= ln(Y_{t}), b_{0}= ln Y_{0}, and b_{1}=

ln(1+g), then our model becomesy

_{t}

= b_{0}+ b_{1}t,which can easily

be estimated using the variable "year" for t and the constructed variable

ln(Y_{t}) as the dependent variable. The steps in SPSS are as follows:

- Select

Transform from the menu bar, then choose Compute. . .;- In the

Target Variable box type lrgdp;- In the

Numeric expression box type ln(rgdp);- 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.

- Select

Data from the menu bar, then choose Select Cases . . .;- Click the

button for Based on time or case range, then click Range;- Type 1948

in the first box and 1996 in the second;- Click OK.
Now, run the regression:

- Select

Statistics from the menu bar, choose Regression, then Linear . . .;- Highlight

lrgdp in the variable list and use the arrow to click it into the dependent

variable box;- Do the

same for year, putting it into the independent variable box;- Click OK.
The estimated equation

is Y_{t}= -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 = e^{0.03238},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)

Y_{t}= -66.5837 + 0.03793(Year), Þ g = 3.87%(1973-1996) Y

_{t}= -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.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:

- 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.- 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%.- Lack of savings

and investment: This is one of the strongest arguments, but then, why did

savings and investment rates fall?- 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.- 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.- 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.- 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

roads, schools, etc.As you can see,

there are a lot of possibilities. This topic remains one of the most important

issues in economics.Baumol, William,

Sue Anne Batey Blackman, and Edward Wolff,Productivity and American Leadership:MIT Press. 1989.

The Longer View.Federal Reserve

Bank of Kansas City,Policies for Long-Run Economic Growth: A SymposiumFRB, Kansas City.

Sponsored by The Federal Reserve Bank of Kansas City.

1992.Maddison, Angus,

Dynamic Forces in Capitalist Development: A Long Run Comparative View.Oxford University Press. 1991.