Correlation Coefficients:
Inflation and Unemployment: The Phillips Curve and all that

In the early 1970s the model of economic growth that had appeared to work since the end of World War 2, finally seemed to have broken down. The Phillips Curve had allowed economic planners to target a certain level of price inflation against an accepted level of unemployment. In this way, socially acceptable levels of macro-economic performance were created within a stable economy.

But the four-yearly (approximately) business cycles began to show a worrying trend - each new economic downturn brought higher levels of unemployment; and each upturn brought ever-increasing levels of price inflation.

So what has happened since then? Are we back to the days of 'certainty' in economic planning, so that the 'socially-acceptable' outcome can be targeted? Or has the Phillips Curve ceased to have relevance in the late 20th and early 21st Century? How can we use correlation coefficients to help us analyse this issue?

We can examine the link between inflation and unemployment over the past 20 years, using the TimeWeb sample data to gather data for UK GDP, inflation and unemployment.

Note that the ILO measurement of unemployment only provides data from 1984. This means that we should only use inflation data for this period. However, the effects of inflation tend to be felt some time after they are recorded. In other words, it takes time for the full impact of price rises to register in an economy. Economists suggest that there is a time lag of about two years between the inflationary pressure being recorded and its impact being felt. So we should build a time lag into our inflation data. Select RPI data for 1982 to 1998 and set it alongside unemployment data for 1984 to 2000.

Firstly, we should place the data for these three variables into a graph. It should look something like this:

Studying the chart it appears that the link between economic growth and inflation/unemployment has changed: Up until 1984 in fact the relationship between GDP and inflation seems to have reversed. Note how RPI-X falls over this period, even though GDP rises. After that, during the period 1988-92, inflation seems to rise just as GDP starts to fall.

But hang on! We haven't built in the time lag into our RPI data yet. Use the data you have to introduce a time lag of two years. Make sure you lag the right variable! Now redraw the graph. It should look something like this:

OK, this seems a little better. Look at the link between GDP and RPI-X; here there is a more direct relationship between the two factors, most notably during the economic recovery of the early 1990s. Notice how from 1991 onwards GDP starts to rise, followed closely by a rise in RPI-X. After this period, though, the relationship seems to change again, with virtually 'flat' lines for both of the variables.

The data for ILO unemployment seems to indicate a more rational link between the jobless rate and the level of economic activity; note that unemployment falls over the period 1984 - 1990 coinciding with consistent levels of economic growth, although the economy moves into recession from 1989. The resulting rise in unemployment is consistent with the fall in GDP growth. This situation reverses itself as the late 1990s brought consecutive years of steady economic growth.

Now let's look for evidence of association between these three variables.

Correlation between GDP and inflation:

Remember that the formula for the product moment correlation coefficient is as follows:

Have a look back at the illustration of product moment correlation coefficient if you are not sure about how to apply this formula.

It will help if you draw up a table using the appropriate data under these headings: RPI inflation (X), ILO unemployment (Y), X-squared, XY and Y-squared. Also, you will need to create a row at the foot of the table to enter the totals for each column. Below is a partially completed version. Try to fill the gaps in the table.

CORRELATION COEFFICENT: GDP:RPI-X

This produces a figure of r = -0.74. Is this what you would expect?

What we need to do is to introduce a two year time lag into the correlation between GDP and RPI-X.

CORRELATION COEFFICIENT GDP: RPI-X WITH TWO YEAR LAG

This produces a coefficient of r = -0.17. Is this what you might expect?

Now you should consider what other relationships between the variables should be investigated. Try to carry out your own correlation analysis for the variables you select.

Summary:

This analysis of correlations between GDP growth and price inflation has produced a set of results that do not live up to our expectations. We would expect that as economic growth increases, greater demand for the factors of production (land, labour, capital and enterprise) result in falls in the level of unemployment. However, as growth continues we would eventually expect to see demand-pull or cost-push inflation increasing.

Rather than these expected results, we have produced correlation coefficients that indicate the opposite. So what can be read into these findings?

There is evidence here that the established link between growth, inflation and unemployment has ceased to have relevance in the period studied. As ever, though, it is hard to define precisely the cause(s) of this change. What must be remembered is that the UK economy has experienced two major recessions in the past twenty years, with short periods of strong economic growth being corrected by severe and prolonged downturns.

The long-lived recession of the early 1980s, followed by the rapid economic growth of the late 1980s and the 'bust' of the early 1990s have shaped the expectations of workers, industries and households. Perhaps we have become adapted to low inflation and temper our wage demands accordingly; maybe the 'supply-side' changes made in the 1980s have enabled the economy to grow at a faster rate without generating cost-push inflationary pressure; alternatively or additionally, perhaps the advances in information technology have enabled a 'new' economy to surface, where above-trend growth can be coupled with low inflation and unemployment.

Whatever the reasons, the period 1980 - 2000 have seen a move away from causes and effects traditionally associated with the UK economy. Detailed analysis of the data using correlation coefficients has given us a much clearer picture than a cursory visual look ever could do, and therefore raised issues about correlation and causation much more clearly.

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