Diebold Ch5/6 Video - Seasonality Regression

[Jared Seguin]

Hi,

I was just watching the video for Diebold chapters 5 and 6 and I am struggling with the seasonality portion. In the example, we consider the case of using dummy variables to indicate the 4 quarters of the year - such that we have D1, D2, D3, and D4. However, by including 4 dummy variables for only 4 categories, do we not introduce multicollinearity to the model?

What I mean by this is that the 4 quarters can be represented by only THREE dummy variables. This is because if D1, D2, D3 are all = 0, this already indicates to us that it is the 4th quarter, without the need of a D4. Inclusion of D4 creates collinearity within the regressors.

Thanks for any help!

J

 

[Jared Seguin]

follow up: nevermind, I just got to the next couple minutes of the video where we do a numerical example and the model is corrected to only use 3 variables. All good.

 

[David Harper CFA FRM]

Hi @Jared Seguin Glad you saw the alternate expression, thanks for the good comment! However, in the first approach (which follows Diebold of course) where the seasonality is modeled with four (4) quarterly variables, please note that no intercept is included, such that perfect multicollinearity is avoided there also. Only when the number of dummy variables is dropped from 4 to 3 is the intercept included (in which case, the intercept effectively represents the coefficient for the first quarter's dummy variable and the other coefficients becomes differences/deltas from this benchmark). So the so-called "dummy variable trap" would be realized if we regressed against all four quarterly dummy variables plus the intercept because then would be manifesting perfect multicollinearity. Please see https://en.wikipedia.org/wiki/Dummy_variable_(statistics) (emphasis mine, but a similar explain is found in Diebold also)

Dummy variables may be extended to more complex cases. For example, seasonal effects may be captured by creating dummy variables for each of the seasons: D1 = 1 if the observation is for summer, and equals zero otherwise; D2 = 1 if and only if autumn, otherwise equals zero; D3 = 1 if and only if winter, otherwise equals zero; and D4 = 1 if and only if spring, otherwise equals zero. In the panel data, fixed effects estimator dummies are created for each of the units in cross-sectional data (e.g. firms or countries) or periods in a pooled time-series. However in such regressions either the constant term has to be removed or one of the dummies has to be removed, with its associated category becoming the base category against which the others are assessed in order to avoid the dummy variable trap [aka, perfect multicollinearity]

 

[Jared Seguin]

Yep , makes perfect sense. Thanks David