# Manufacturing's Lack of Confidence

Other developed market PMIs tend to have a positive correlation with the Euro area PMI, such as the PMI for Japan and the U.K. Both have correlations of greater than 0.8. The average for these two country PMIs is shown on the dotted line of the chart below. As the January Euro area PMI rose 1.2, to 53.9, we would also expect somewhat of a further expansionary reading in the January PMIs of Japan and the U.K. And this is despite the drop in China's PMI.

Another way to look at this is to allow for the computer machine to cluster country PMIs that influence other country PMIs. We introduced some of these concepts in this note, and we can mathematically think of this as a broader covariance problem where we consider the actual economic weights instead of regression weights. The influence of pairing combinations of regional PMIs together, incorporating the economic weight of the influential candidate region, can be expressed through a second derivative function of the combined regional PMIs, which would be the two intersections on a covariance matrix.

The covariance matrix looks at all combinations of a set of regional PMIs and any other influential candidate PMI that is not already included. This covariance we are seeking is also equal to the correlation multiplied by two dispersions. And to get to the beta, we simply divide by the deviation of the initial regional PMI and multiply out by the influential candidate PMI. Now we know that we are looking at the covariance fit so we need to multiply by the proportional economic weights provided by the initial regional PMI group and the influential candidate PMI set.

This entire optimization process shown in the regression charts above doesn't lead to much additional insight except for India. The algorithm solves to show that while the Euro area PMI mathematically has a negative linear relationship with the India PMI, India's PMI is economically more connected to the changes in the U.S. PMI.

This entire analysis shows that the PMI analysis is more than one where either the emerging markets (or the U.S. in isolation) are negatively risking other regional PMIs. Instead we see that the U.S. and China together have influenced other emerging markets. But the PMIs for other developed markets are much more influenced by other factors similar to those related to the Euro area PMI. Sure, we are in a position this year where two large January PMIs have suddenly contracted, but there are still limits -- as we have shown -- to how much that would affect the positive trend in other regional PMIs, particularly in developed markets.

At the time of publication, the author held no positions in any of the stocks mentioned.

This article represents the opinion of a contributor and not necessarily that of TheStreet or its editorial staff.

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