Kerry up, markets down? A regression analysis

In the August 11, 2004 issue of the Wall Street Journal, an article by Eric Engen (resident scholar at the American Enterprise Institute) entitled “Kerry Up, Markets Down” appeared which makes the following claim: “…Sen. Kerry has promised to repeal a significant portion of (the Bush) tax cuts if elected, including the tax rate reductions on dividend and capital gain income. With the growth rate of the economy high but slowing somewhat, there are signs that this promise is rattling financial markets. The evidence suggests that when Sen.Kerry’s political fortunes rise, the stock market tanks.” Steve Forbes, editor in chief of Forbes and former (Republican) presidential candidate, weighed in with a similar opinion piece (entitled “The Rubinian Candidate”) in today’s Wall Street Journal.

Mr. Engen’s analysis is based upon graphically comparing 5 day moving averages of the 2004 US Presidential “Winner Takes All” Kerry Futures Contract Prices with 5 day moving averages of the S&P 500 index. While it appears that the two time series move in opposite directions, a more convincing analysis requires determining whether what seems visually apparent is statistically significant. Experimental evidence shows that people tend to see order even when the charts they are looking at consist of randomly generated numbers. Therefore, I computed daily returns on the S&P 500 and the Kerry Futures contract and regressed stock returns on Kerry Futures contract returns for the period June 2, 2004 through August 9, 2004. I selected this period because the data source (the Iowa Electronic Markets database) has a continuous price history on the Kerry Futures contract which began on June 1, 2004.

The regression equation that I estimated is specified as follows:

rS&P500,t = a + brKerry,t + et,

where rS&P500,t = daily return on the S&P 500, rKerry,t = daily return on the Kerry Futures contract, a = intercept, b =slope; and et= error term. The following table summarizes the regression statistics:

Regression Statistics

R2

0.0680

Parameter

Coefficients

Standard Error

t Stat

P-value

a

-0.0010

0.0010

-0.9972

0.3240

b

-0.0389

0.0215

-1.8122

0.0766

This regression equation has (as one would expect) a relatively low coefficient of determination, or R2 of only .068. In other words, there are other (probably much more) important determinants of stock market returns other than the odds of a Kerry presidency. Furthermore, since 1) the sign of the regression coefficient associated with returns on the Kerry Futures contract is negative, and 2) the correlation coefficient between the dependent and independent variable in a univariate regression equation equals the square root of the coefficient of determination, this implies that the correlation coefficient between returns on the Kerry Futures contract and the S&P500 index is -.26.

Two important questions remain: 1) is the effect statistically significant and 2) is the effect economically significant? The answers to these questions are 1) yes, and 2) no.

Let’s look first at the question of statistical significance. Whether a particular independent variable is statistically significant depends upon the P-value associated with its regression coefficient. A regression coefficient’s P-value indicates the probability of “Type 1” error. Type 1 error occurs whenever one concludes that a relationship exists when in fact it does not. Furthermore, one must differentiate between “1 tail” and “2 tail” tests. The P-values listed here are for 2 tail tests, meaning that the “null” hypotheses we are trying to reject are a = 0 and b = 0. In the case of Engen’s theory, since the null hypothesis we are trying to reject is that b is non-negative, a 1 tail test is more appropriate. Consequently, based upon these test statistics, we would conclude that a is not statistically different from 0, and that the negative relationship between returns on the Kerry Futures contract and the S&P500 index is statistically significant (at the 7.66%/2 = 3.83% level). Technically, the 1 tail P-value of 3.83% suggests that the probability of committing Type 1 error (i.e., concluding that a negative relationship exists when in fact it does not) is very small.

Next, consider the economic significance of the effect. Even though it is statistically significant, the actual magnitude of the effect is quite small. Specifically, on average, a 1 percent change in the value of the Kerry Futures contract is associated with a -0.0389% change in the value of the S&P500 index. Based upon this result, I would have to conclude that Mr. Eng
en’s basis thesis (that when Sen. Kerry’s political fortunes rise, the stock market “tanks”) does not represent a particularly fair characterization of this relationship. There is an inverse relationship, but the economic significance of the effect is rather negligible.

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