Why This Econometric Model Is Useful

                    

                               

                          This discussion is for our readers who are familiar with econometrics.

                                                                        

 

Our assumption of a zero intercept differs from the usual econometric practice of running the OLS model in the form:

 

                                                            Y = mx + b

 

where b is the intercept, to account for other variables which might have been omitted.

 

By analyzing the ratio of the two economic quantities  (Bond Yields/Stock Earnings Yields), we turn an

intractable stock market analysis problem into a tractable one because the many factors common to

both stock and bond investments cancel out, leaving us with the much simpler problem of deciding

what fewer factors affect the willingness of people to invest in stocks, rather than in bonds.

 

Having justified on this theoretical ground the choice of a simpler model in the form: Y = mx, assuming

no intercept, we then run into a possibly knotty statistical problem by having forced the regression

equation through the origin. In the usual unconstrained case, the expected error of  the regression

equation is equal to zero. In the contrained case, this expected error might not be equal to zero,

causing problems with the calculation of R2, the goodness of fit statistic for the regression.

 

Standard econometric computer programs calculate R2 by using statistical moments calculated from the

mean of the data. This is a valid procedure for a zero intercept regression only if the mean of the data 

falls exactly upon the calculated regression line (Aigner, 1971, p.p. 85-92). As it turns out, for the years

(1968-1999):

 

       Average:                

Bond Yields/Stock Earnings Yields

=

1.34

 

Capacity Utilization (t+1)

=

80.13

 

Inflation (t+1)

=

5.01

 

Calculating Bond Yields/Stock Earnings Yields from the regression equation:

                

                 Bond Yields/Stock Earnings Yields = .022 * cap util (t+1) - .079 * infl (t+1)

                 Bond Yields/Stock Earnings Yields = 1.37, say 1.34

 

The mean of the data lies upon the calculated regression line, and the computer calculated R2 statistic

of .954 is appropriate.

 

In the most general zero intercept case, Aigner (1971) recommends calculating R2 by using the raw

statistical moments calculated as deviations from zero, rather than from the mean of the data. Using this

method, our regression equation explains 100% of the variation in the data, with a R2 = 1, that is:

 

                                                               RSS =  60.43

                                                               TSS =  60.34, say 60.43