If you are downloading this SHAZAM code for use on your own computer, select "File", then "Save As...", and save on your own diskette (a:) or your own hard drive (c:\) using the same filename e143sh13.sha.

IMPORTANT: you must then use an editor (like TED) to delete all of the HTML code from the top and the bottom of the file, leaving only the SHAZAM code. The line which reads "* SHAZAM code (e143sh13.sha) downloaded from UCLA Econ 143 (CAMERON) WebSite" should be the first line of your edited program file. Save the edited program as wtsize.sha

* SHAZAM code downloaded from UCLA Econ 143 (CAMERON) WebSite: 
* HTML file called e143sh13.htm, and should have 
*  been downloaded as wtsize.sha

*--------------------------------------------------------------
* EXAMPLE OF ORDINARY MULTICOLLINEARITY SITUATION
* DATA IN  n:wtsize.dat CONSIST OF TWENTY OBSERVATIONS ON EACH OF FIVE
* VARIABLES:  Q (quantity demanded), P (price), TAX (sales tax paid),
* WT (weight of product) and SZ (size of product).  
* THIS STYLIZED EXAMPLE IS MEANT TO BE A DEMAND FUNCTION FOR A HETEROGENEOUS
* COMMODITY, WHERE ATTRIBUTES OF THE COMMODITY (NAMELY WEIGHT AND SIZE)
* ALSO INFLUENCE QUANTITY DEMANDED.

sample 1 20
*read(n:wtsize.dat) q p tax wt sz
read(wtsize.dat) q p tax wt sz

* run the "kitchen sink" regression of q on everything else: explain
*  what happens
ols q p tax wt sz

* if you don't know already, check the correlations among the variables
* to see if there is a perfect multicollinearity problem anywhere;
* explanatory variables should be "scattered widely across the floor"
* of the regression model, not lying too closely along some line.
stat p tax wt sz / pcor
plot p tax
plot p wt
plot p sz
plot wt sz

* leave out the variable that doesn't add any extra information;
* given that tax is always 0.08*price, it is not possible in these
* data to ascertain the separate influence of price changes without tax
* changes, or tax changes without price changes...but maybe people only
* think of the gross price of things anyway, and these would have the
* same marginal effects on demand.
* check the statistical significance of the individual slope coefficients.
* check the R-squared value...is it consistent with the t-ratios?
ols q p wt sz
* do an F-test of the joing contribution of the three explanatory variables.
test
test p=0
test wt=0
test sz=0
end

* see if individual variables have any effect (but beware of omitted
* variables bias in the estimated coefficients in this simple regression)
ols q p
ols q wt
ols q sz

* try pairs of variables (note what happens to coefficient on first
* variable as second variable is added--order irrelevant, of course).
* check the correlations between the estimated coefficients in each
* regression model---different thing than the correlations among the
* variables used in the model
ols q p wt / pcor
*confid p wt / gnu lineonly
confid p wt 
ols q p sz / pcor
*confid p sz / gnu lineonly
confid p sz
ols q wt sz / pcor
*confid wt sz / gnu lineonly
confid wt sz

* the confidence ellipses above provide the set of plausible joint
* hypotheses about the estimated coefficients; the rectangles are the
* intersection of plausible individual hypotheses...the marginal
* confidence intervals "spread out"--their overlap.  NOTE that some
* plausible joint hypotheses are rejected individually, and vice versa.

* find the probable source of the multicollinearity problem by running
* auxiliary regressions:  Problems among the regressors in the main model
* are evidenced by high R-squared values in these auxiliary regressions--
* high t-ratios in these models indicate the most likely culprit variable
* subsets

* NOTE the dependent variable in each of these regressions:
ols p wt sz
ols wt p sz
ols sz p wt

* SHAZAM is so sure you might want to do this sort of exploration that a
* special option on the "main" regression does these auxiliary regressions
* for you and reports the most interesting results:  the AUXRSQR -
* auxiliary R-squared option

ols q p wt sz / auxrsqr

* check the output to see which explanatory variables can be really 
* accurately represented by some linear function of the others.

* since p and wt are highly correlated, these are where you have to focus
*  your attention in dealing with the multicollinearity problem.

* a.)  if you aren't primarily interested in dq/dp or dq/dwt, but are most
* interested in how q is affected by variations in sz, you could probably
* drop one of p or wt and leave the remaining variable in this pair to
* capture the influence of both of them on q.  This would ensure that your
* estimate of dq/dsz is not contaminated by omitted variables bias.
* Check the distortion in the coefficient on sz if neither p nor wt is
* included in the regression.
ols q p sz

* in the above regression, the coefficient on p is really the combined effect
* due to changes in p and that portion of the change in wt that "moves
* similarly" to p in your sample

* b.) you could go out and collect data on demand for other variants of this
* commodity for which p and wt are not so closely correlated.  If price is
* higher when weight is lower, for example, you would want to include extra 
* observations for cases where the commodity is heavy but still expensive,
* or light but cheap in spite of this.

* c.) you might be able to get an approximate value for the price derivative
* from some other study, and impose this on the model.  Estimate weight
* effect separately.

* d.) may have to just give up trying to get separate weight and price effects
* from this data set.