The following discussion will show that there exists a strong correlation between the size of the United States' national dept and the value of the DJIA. It will also be shown that it may be possible to use this correlation to predict how low the DJIA will fall during a market correction. To accomplish this, we will examine the market correction of 1987, 2002 and the possibly current one of 2007.

I first noticed the correlation between the size of the national debt and the DJIA during 1995 and was surprised at how using the national debt to predict the DJIA seemed to explain the market correction of 1987. However, this was an explanation found after the fact and could have been a fluke. Therefore, when the market began to turn downward in 2002, I dug the numbers back out, updated them and performed new calculations to see if I could predict where the DJIA would end up in 2002. I ended up predicting it would fall to around 7500 to 7600. I told my prediction to just one person and he thought my predicted value was far too low. However, when the DJIA fell to its 2002 low of 7286.27, I began to think the model might in fact have some predictive value. Therefore, before the market can fully correct itself this time around, I am presenting my analysis publicly for all to see. The proof, as they say, will be in the pudding.

It should be pointed out from the start that the size of the national debt in and of itself would not seem to be a good explanation of movement in the DJIA. However, the national debt does appear to be a good "catch all" variable for explaining movement in the DJIA since the national debt is highly correlated with many other economic variables such as Gross Domestic Product and inflation. A proper analysis would attempt to sort all of the many variables out and include them in the prediction equation. I'm sure such attempts have been made in the past by other people, but for our puposes here we will simply use the national debt as a dummy variable to fill in for all of the other variables with which it is correlated.

The first row of numbers in Table 1 shows the correlation coefficients between the size of the national debt and key DJIA values for the years 1955 to 1987. Assuming the size of the national debt affects the value of the DJIA and may take time for its effect to occur, the second row in Table 1 is the correlation values between the size of the national debt from 1955 to 1986 with the annual DJIA values from 1956 to 1987 (a one year lag). Similarly, the third row in Table 1 is the correlation values between the size of the national debt from 1955 to 1985 with the annual DJIA values from 1957 to 1987 (a two year lag).

As can be seen from Table 1, there is a very strong correlaton between the size of the national debt and the value of the DJIA. In case the above results were simply the results of having happened to choose just the right starting period, Table 2 shows the same results with 1965 being used in place of 1955 as the starting year. As can be readily seen, the results were pretty much the same.

The above results led me to wonder what would happen if I was to use the size of the national debt to predict the value of the DJIA. A simple regression model for this would take the form:

In the above equation, 'a' is the Y intercept value, 'b' is the slope and 'ND' is the size of the national debt.

First I should explain that the model being used here would result in a straight line sloping upwards toward the right and intersecting the vertical axis. However, you will notice that the yellow line in the charts below, which represents our predicted values, has a upward curve to them. This is due to performing a separate calculation of the model for each year using the DJIA's midrange value as the dependent variable for making the prediction. In other words, to find the predicted midrange value of the DJIA for 1965, the years 1955 through 1965 were used, the years 1955 through 1980 were used to predict the DJIA value for 1980, and so on.

Running four versions of the model to determine the predicted value of the DJIA's high, low and midrange for 1987 gives the results shown in Table 3. In calculating each value, the DJIA's values fron 1955 through 1987 are used as the dependent variable and the size of the national debt is used as the independent variable. The top row in Table 3 gives the DJIA's actual values in 1987, the second row gives the predicted value, the third row gives the level of statistical significance, while the fourth row shows the percentage by which the prediction missed the actual value.

The statistical significance levels in row three of Table 3 shows that the results are hignly significant. For example the equation for predicting the DJIA's midrange is statistically significant at the 0.007804 level, i.e. we could expect this to be the result of random chance less than 1 time in a hundred. The predicted high of the DJIA for 1987 is the weakest in terms of statistical significance, yet even it shows that the odds of getting the results purely by chance are less than one in 10.

The percentage by which the actual values missed are shown in the fourth row of Table 3 and seem to show significant misses in our prediction ability. However, take a look at Chart 1 and the predictive ability of the model is much nore apparent.

During 1987 the DJIA ranged from a high of 2722.42 to a low of 1738.74. This represents a 36.1% drop in the DJIA from its high. In Chart 1, the DJIA's high value can be seen to move well above the predicted midrange value (as well as the predicted high of 2098.08 shown in Table 3.). The DJIA's drop in 1987 to a low of 1738.74 placed it only 68.68 points below the predicted midrange value of 1807.42 (see Table 3) and 221.98 points above the predicted low (see Table 3). Chart 1 also shows that the following year (1988) the DJIA's high and low both remained close to the predicted midrange value.

Chart 1

Prior to the market correction of 2002, the DJIA had reached its all-time closing high of 11722.98 on January 14, 2000. The DJIA reached its lowest close during this market correction on October 9, 2002. So the market correction in this case was a long slow one stretched over nearly 34 months.

Table 4 shows the correlation coefficients between the size of the national debt and the DJIA's High, low, close and midrahnge from 1955 through 2002. As can be seen these correlations are even stronger than the correlations for 1955 through 1987 (shown in Table 1). Part of the improved strength of the relationship could well be due to the simple fact that the sample is now bigger - covering 48 years compared to 33 years.

Table 5 shows the actual and predicted values of the DJIA for 2002, as well as the statistical significance level of each predition and the percentage by which it was off. We already saw that for 1987 the model estimated the DJIA's low to be 221.98 points lower than it actually was. In 2002 the predicted low was only lower than the actual DJIA low by 269.41 points, or 3.8%.

Chart 2 shows the results of the model up through 2003. Similar to the 1987 correction, the DJIA can be seen in Chart 2 to be rising far above its predicted midrange value throughout the late 1990s, peaking in 2000 and then falling for the next couple of years. During the same time period, the DJIA's low for each year can be seen as rising well above the predicted midrange value. By the time the correction had bottomed out at 7286.27 in 2002, the DJIA's low was back under the predicted midrange's value as it should be and the high was also much more in line with predictions. From its closing high of 11722.98 on January 14 2000, to its low of 7286.27 on October 9, 2002 the DJIA fell 4436.71 points (37.8%). Actually, the low in 2002 was 7,181.47 on October 10, but 7286.27 was the DJIA's lowest closing value, which it hit on October 9.

Chart 2

As can be seen from the correlation coefficients in Table 6, the correlations between the size of the national debt and the values of the DJIA from 1955 through 2007 is even stronger than in the earlier cases. A correlation of .95 is nearly a perect correlation and means that the model explains 90% of the variance in the data. (The square of the correlation gives you the percentage of the variance explained by the model.)

As can be seen from Table 7, the correlations are also statistically significant. The good news is there does not appear from the model to be any reason to expect another drop like the 36.1% drop in 1987 or the 37.8% drop between 2000 and 2002. The worst that might be expected in 2007 is a drop from the high of 14021.95 to the predicted low of 10782.17, i.e., a 23.1% drop.

Based on the corrections of 1987 and 2002, I would expect the DJIA to drop to a low somewhere between the predicted low of 10,782.17 and the predicted midrange value of 11,998.43. Therefore, my formal prediction (which I am making on August 17, 2007 with the DJIA having closed today at 13,079.08) is to not be buying any stocks until the DJIA drops below 11,400.

Last, but not least, it should also be pointed out that the 2007 value used for the national debt was an estimated value taken from www.brillig.com/debt_clock/ on August 17, 2007, since no official numbers yet exist for 2007.

Chart 3

The high correlation between the size of the national debt and the DJIA makes the size of the national debt a good variable for predicting when the stock market is becoming overheated and for predicting how low the DJIA must fall to get back to a "proper" value range. It certainly cannot predict how overvalued the market may become, but it can serve as a warning when the market starts to fall that you need to get out of it and suggest a general valuation range as to when it would be a good time to get back into the market.