Ok, not sure if I correctly followed up on your suggestions, but this is what I have done:
Using the regression coefficient estimates that I obtained for c, beta1Y, beta2Y, beta3Y and beta4Y (obtained by running the regression "Yt = c + [beta1Y]Xt + [beta2Y]Xt-1 + [beta3Y]Ct + [beta4Y]Yt-1 + errorterm"), I 'reverse engineered' a beta1Y-value for each time t. Thus, for each t I determined:
[beta1Y]t = (Yt - (c + [beta2Y.regressionestimate]*Xt-1 + [beta3Y.regressionestimate]*Ct + [beta4Y.regressionestimate]*Yt-1)) / Xt
Similarly, I determined [beta1Z]t-values for each t, resulting in having two time series; of beta1Y and beta1Z. Now the variance of (beta1Y - beta1Z) can straightforwardly be computed in Excel by first creating a new time series: "beta1Y - beta1Z", but alternatively I can indeed also do what -I suppose- is what you have been suggesting: seperately determine the variance for the beta1Y and the beta1Z time series, as well as the covariance for the beta1Y and beta1Z time series, and subsequenlty compute the variance for (beta1Y - beta1Z) by using the formula: VAR(beta1Y)+VAR(beta1Z)-2*COVAR(beta1Y,beta1Z). These two approaches yield almost identical variance.of[beta1Y-beta1Z] values.
Should I now execute the t-test as:
t= (mean[beta1Y.timeseries] - mean[beta1Z.timeseries]) / SQRT(variance.of[beta1Y - beta1Z])
Or should I maybe compute:
t = (beta1Y.regressionestimate - mean[beta1Z.regressionestimate]) / SQRT(variance.of[beta1Y - beta1Z])
Or something else? (not sure exactly what t-test formula to use now..)
Neither of the above test formulae yield a t-test value that is anything close to significant. Intuitively this seems very unlikely for my sample as the t-statistic values reported for the beta1Y.regressionestimate equals 3,160 and for the beta1Z.regressionestimate 1,720. Intuitively I would say beta1Y must thus be (at least close to being) 'significantly more significant' than beta1Z.
(Consequently I would suppose I am ought to use another t-test formula, or that I am simply making some mistake; possibly I am forgetting to divide/multiply by n somewhere in the above formulae?)
Hopefully you're still following me? Please tell me if I need to clarify anything.
Again, your insights and help are really appreciated.. Many, many thanks