In recent years a controversy has been brewing among economists about the resurgence of U.S. productivity in the second half of the 1990s. One school of thought argues that the United States had developed a “new economy” based on the extraordinary advances in communications and information technology of the 1990s. The most optimistic proponents argue that it would generate higher average productivity growth for decades to come. The pessimists, on the other hand, argue that even five or ten years of stronger productivity growth does not prove that higher productivity will last for the long term. It is hard to infer anything about long-term productivity trends during the later part of the 2000s, because the steep recession of 2008–2009, with its sharp but not completely synchronized declines in output and employment, complicates any interpretation.

Productivity growth is also closely linked to the average level of wages. Over time, the amount that firms are willing to pay workers will depend on the value of the output those workers produce. If a few employers tried to pay their workers less than what those workers produced, then those workers would receive offers of higher wages from other profit-seeking employers. If a few employers mistakenly paid their workers more than what those workers produced, those employers would soon end up with losses. In the long run, productivity per hour is the most important determinant of the average wage level in any economy. To learn how to compare economies in this regard, follow the steps in the following example.

COMPARING THE ECONOMIES OF TWO COUNTRIES

The Organization for Economic Co-operation and Development (OECD) tracks data on the annual growth rate of real GDP per hour worked. You can find these data on the OECD data webpage “Labour productivity growth in the total economy” at this website.

Step 1. Visit the OECD website given above and select two countries to compare.

Step 2. On the drop-down menu “Variable,” select “Real GDP, Annual Growth, in percent” and record the data for the countries you have chosen for the five most recent years.

Step 3. Go back to the drop-down menu and select “Real GDP per Hour Worked, Annual Growth Rate, in percent” and select data for the same years for which you selected GDP data.

Step 4. Compare real GDP growth for both countries. Table 6.2 provides an example of a comparison between Australia and Belgium.

Nothing is more important for people’s standard of living than sustained economic growth. Even small changes in the rate of growth, when sustained and compounded over long periods of time, make an enormous difference in the standard of living. Consider Table 6.3, in which the rows of the table show several different rates of growth in GDP per capita and the columns show different periods of time. Assume for simplicity that an economy starts with a GDP per capita of 100. The table then applies the following formula to calculate what GDP will be at the given growth rate in the future:

For example, an economy that starts with a GDP of 100 and grows at 3% per year will reach a GDP of 209 after 25 years; that is, 100 (1.03)²⁵ = 209.

The slowest rate of GDP per capita growth in the table, just 1% per year, is similar to what the United States experienced during its weakest years of productivity growth. The second highest rate, 3% per year, is close to what the U.S. economy experienced during the strong economy of the late 1990s and into the 2000s. Higher rates of per capita growth, such as 5% or 8% per year, represent the experience of rapid growth in economies like Japan, Korea, and China.

Table 6.3 shows that even a few percentage points of difference in economic growth rates will have a profound effect if sustained and compounded over time. For example, an economy growing at a 1% annual rate over 50 years will see its GDP per capita rise by a total of 64%, from 100 to 164 in this example. However, a country growing at a 5% annual rate will see (almost) the same amount of growth—from 100 to 163—over just 10 years. Rapid rates of economic growth can bring profound transformation. (See the following feature on the relationship between compound growth rates and compound interest rates.) If the rate of growth is 8%, young adults starting at age 20 will see the average standard of living in their country more than double by the time they reach age 30, and grow nearly sevenfold by the time they reach age 45.

Table 6.3. Growth of GDP over Different Time Horizons

HOW ARE COMPOUND GROWTH RATES AND COMPOUND INTEREST RATES RELATED?

The formula for growth rates of GDP over different periods of time, as shown above, is exactly the same as the formula for how a given amount of financial savings grows at a certain interest rate over time. Both formulas have the same ingredients: an original starting amount, in one case GDP and in the other case an amount of financial saving; a percentage increase over time, in one case the growth rate of GDP and in the other case an interest rate; and an amount of time over which this effect happens.

Recall that compound interest is interest that is earned on past interest. It causes the total amount of financial savings to grow dramatically over time. Similarly, compound rates of economic growth, or the compound growth rate, means that the rate of growth is being multiplied by a base that includes past GDP growth, with dramatic effects over time.

For example, in 2012, the World Fact Book, produced by the Central Intelligence Agency, reported that South Korea had a GDP of $1.64 trillion with a growth rate of 2%. We can estimate that at that growth rate, South Korea’s GDP will be $1.81 trillion in five years. If we apply the growth rate to each year’s ending GDP for the next five years, we will calculate that at the end of year one, GDP is $1.67 trillion. In year two, we start with the end-of-year one value of $1.67 and increase it by 2%. Year three starts with the end-of-year two GDP, and we increase it by 2% and so on, as depicted in the Table 6.4.

Table 6.4 End-of-year Two GDP, 2012

Another way to calculate the growth rate is to apply the following formula:

Where “future value” is the value of GDP five years hence, “present value” is the starting GDP amount of $1.64 trillion, “g” is the growth rate of 2%, and “n” is the number of periods for which we are calculating growth.