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, Y_t equals:

Y_t = 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(Y_t ) = ln(Y₀(1+g)^t) =
lnY₀ + ln(1+g)^t =
lnY₀ + t*ln(1+g).

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

y_t = b₀ + b₁t,

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:

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 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.

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 roads, schools, etc.

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.

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