Measuring the Standard of Living

Economists want to be able to make statements that compare the standard of living between different countries or between different time periods.  This is quite tricky.  As we have just observed, people enjoy a very different mix of products and services at different points in time.  In fact, a likely reason that DeLong seized on the example of flour is that flour is one of the few products that we buy today that we can picture being purchased 500 years ago.

Economists estimate the average standard of living in a particular year in a particular country by taking the total value of goods and services produced in that country in that year and dividing by population.  The total value of goods and services produced is called real Gross Domestic Product, or real GDP.  The ratio of GDP to population is called GDP per capita.  GDP per capita is the usual measure of the standard of living.

GDP is usually measured in dollars.  Although the Japanese might measure their GDP in yen, we would convert their GDP to dollars in order to compare it to ours.  We can do such a conversion by using the yen/dollar exchange rate, the rate at which you can trade yen for dollars.

When we compare GDP across time, we want to adjust for inflation, which is a general change in prices.  If we produced 100 bags of flour at a price of \$0.50 each last year, and this year we produce 100 bags of flour at a price of \$1.00, how much did our GDP go up?

If you said that our GDP doubled from \$50 to \$100, then you were calculating nominal GDP, which is the total dollar value of goods and services.  Nominal GDP is a misleading measure of the standard of living.  Because we produced the same 100 bags of flour each year, we would say that real GDP--the physical production of goods--was exactly the same as last year.

To arrive at real GDP, we adjust nominal GDP for price changes.  We pick one year as a base year, and then we measure price changes relative to that base year.  If last year was the base year, then real GDP in the base year was \$50.  Since the price of flour went up from \$0.50 to \$1.00, we say that the price level doubled this year, so that our GDP price deflator is 2.0.    We can divide nominal GDP in any given year by that year’s GDP deflator to arrive at real GDP.  Thus, we divide \$100 by 2.0 to obtain the correct \$50 figure for real GDP.

The following is an important relationship:

Real GDP = Nominal GDP/GDP Deflator

In general, an increase in nominal GDP has two components.  One component is the increase in real GDP, which raises the average standard of living.  The other component is average inflation, which does not raise the average standard of living.  In an economy with many goods and services, the increase in the implicit GDP deflator from one year to the next is a measure of average inflation.  Inflation is a general increase in the prices of goods and services.

The foregoing relationship can be summarized as:

growth in nominal GDP = growth in real GDP plus growth in inflation

The average standard of living in a country is defined as its real GDP divided by population, or real GDP per capita.  This measure of the standard of living is closely related to labor productivity, which is defined as real GDP divided by the total number of hours worked.  By definition,

Standard of living = real GDP/population

Labor productivity = real GDP/hours worked

Then algebraically we have

real GDP/population = (real GDP/hours worked) (hours worked/population)

We can call the ratio of hours worked to population the employment ratio.  Therefore, the standard of living is equal to productivity multiplied by the employment ratio.  Thus, we can raise the standard of living by raising the employment ratio.  However, that is an artifact of the way that GDP only measures goods bought and sold in the market.  It does not include leisure, and it does not include household work, as when a parent stays home to take care of the children or when homeowners repaint their house themselves.

Other things equal, an increase in the employment ratio ought to be regarded as a reduction in the quality of life.  It means that people are working harder.  Thus, even though the ratio of output to population is commonly used to measure the standard of living, a good argument can be made that productivity (the ratio of output to hours worked) is more closely related to the real quality of life.  Thus, one could say that it is more meaningful to compare labor productivity across time and across countries than to compare the standard of living.

On the other hand, the employment ratio can change because of demographics.  If there is an increase in either the very old or the very young, that will mean more people for the working-age population to support.  This will show up as a low employment ratio, and the reduction it entails for the standard of living is real.

The magnitudes output, hours worked, and population tend to grow geometrically.  That is, over a period of several years, the average annual percentage increase is more likely to be constant than the average annual numerical increase.  Suppose that you were to observe population each year obeying this sequence: 100 million, 103 million, 106.09 million, 109.27 million, 112.55 million, and so on.   You could describe the average increase arithmetically as 3.14 million per year or geometrically as 3.0 percent per year.  However, the 3.0 percent per year figure is more accurate.