# Testing of the Phillips Curve

## By Thomas Gunner Arnson

### December 11, 2002

The Phillips curve shows the inverse relationship of the unemployment rate and the inflation rate.  I will examine this relationship in Germany, Japan, and the U.S. over the last 40 years.  In my project, I will examine the data from a limited view due to unknown data required to fulfill the modern Phillips Curve equation, which depends on expected inflation, supply shocks, and cyclical unemployment.  I will try to explain the data using the statistics that are available on the inflation and unemployment rates, while using linear regression to determine if the Phillips Curve hypothesis is correct.

To determine whether each country’s data fit the hypothesis of the Phillips Curve, each country’s unemployment rate and inflation rate were graphed to show the relationship between them.  The x-axis contained the unemployment rate and the y-axis contained the inflation rate.  The linear regression line was calculated and shown within the graph of the original data points.  Using the t-test for correlation with the critical value approach, each country produced a t-value that allowed for the rejection or acceptance of H0.  These calculations are attached in the appendix.  Using this data found from the linear regression, I was able to determine how each country fit the Phillips Curve hypothesis.

Using the t-test, each country produced a different test statistic.  The critical value for a left tailed test with degrees of freedom, n-2, and with 5% significance, t0.05, is

-1.833.  If the value of the test statistic falls into the rejection region (t < - 1.833), reject H0, the null hypothesis that represents non-correlation between unemployment and inflation.  The results of the -test were: Japan = - 4.45, Germany = - 2.42, and the United States = - 1.67.  Japan and Germany’s test statistics fall into the rejection region, while the U.S. does not.  For Japan and Germany, unemployment and inflation are negatively correlated as predicted by the Phillips Curve.  Their degree of correlation differs, however, with Japan having a higher correlation than Germany due to their test statistics.  The U.S., however, had a t-statistic of – 1.67 so H0 is not rejected.  Unemployment and inflation are not negatively correlated for the U.S., at least not in a predictive relationship predicted by the Phillips Curve.

Japan was the country whose data best fit the Phillips Curve.  Generally, the inflation rate has been decreasing over the last 40 years while the unemployment rate has been increasing slightly.  The changes in unemployment and inflation are not as great as the other two countries.  As shown by the linear regression, a general relationship is present, but the effective change is not always the same.  At some points where unemployment is the same value, inflation is higher than a previous year.  This may be due to many economic factors and random disturbances.  During the 1970s, there was some fluctuation and a large increase in the inflation rate without a drop in unemployment.  But a general relationship is present and this correlation with the Phillips Curve is the strongest out of the three countries.

Germany’s data from the linear regression is similar to that of Japan; however, the data is not as strongly correlated as shown by the differences in their t-statistics.  The slope of the regression line is not as steep as Japan, but a general relationship takes form.  Germany is more sporadic than Japan in relation to predictions made by the Phillips Curve.  There are more points where the unemployment rate is the same but the inflation rate is different, either higher or lower than another year.  These points make the data points correlate less with the Phillips Curve

Japan and Germany have correlations with the prediction of the Phillips Curve, but the U.S. has the weakest data that correlates with the Phillips Curve.  The hypothesis of the Phillips Curve predicts a negative relationship between inflation and unemployment; however, the linear regression shows a slightly positive relationship between the two over the last 40 years.  The data is scattered in a different pattern than is found in Japan or Germany.  There are many points where the unemployment rate is the same, but the inflation rate is different.  The U.S. has the greatest number of these points and the frequency of these occurrences results in the shape of the graph.  There is not a shape that is similar to the Japan or Germany.  The regression shows that the U.S. does not correlate with the predictions of the Phillips Curve.

So, is the hypothesis of the Phillips Curve correct?  From this analysis, it is difficult to accurately state yes or no.  Over the last 40 years, Germany and Japan have shown a general correlation with the Phillips Curve.  There have been fluctuations due to random disturbances, supply shocks, and changes in economic policy that may have affected either unemployment, inflation, or both.  The U.S. does not follow the predictions of the Phillips Curve.  At times, some of the data does correlate, but the regression shows that this relationship is very strong.  What accounts for such this departure from Germany and Japan’s correlation?  The differences in fiscal and monetary policy, in supply shocks, and in the relationship of each economy on the global scale may have affected the relationship.  The data may have been more accurate using more advanced methods and employing aspects of the modern Phillips Curve, but this analysis does not have access to all the data.  The predictions of the Phillips Curve are correct .

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