Hi, some advice please on Example 2, page 325. The sample used was for 450 MNCs from 1998 to 2003. My understanding is:
Cross-sectional linear regression: n = number of observations, eg number of companies
Time series linear regression: n = number of observations, ie number of time periods
In this case, it is a combination of a cross-sectional and time series regression, so why is n = 450 instead of n = 450 companies * 5 years = 2,250?
Thanks in advance for your help.
Don’t have the books (thankfully) but 1998 to 2003 is 6 years. Your logic is accurate though - about using number of companies x # of years (unless the variables are averaged over the 6 years).
Thanks CMLSML. They don’t mention anything about averages, and in fact have a subscript t for each time period.
What are the variables being analyzed and the proposed model for the problem?
The example tries to estimate Tobin’s q based on the 450 MNCs with political risk, size, leverage ratio, stock beta, S&P transparency score and geographic diversification of sales as predictors. When calculating the t-statistic for one of the predictors, the example assumes 450 observations and 7 coefficients, df = 433. Each of the independent variables has subscripts i for company and t for time.
Sounds to me as though df should be 442 (= 450 − (7 + 1)).
Maybe there’s some subtlety we’re missing.
Unfortunately, I have only the 2016 curriculum books, and they don’t have this example.
So, Tobin’s Q (and all the other variables) are things measured to describe a company (not a year by itself, so it’s not a time series). It might be helpful to remember that any sample comprises experimental units, and an experimental unit is the object upon which measurements are taken (in other words, we’re measuring characteristics of something, the “something” is our experimental unit). The experimental unit is a company, and you’ve got 450 MNCs (450 experimental units). Sample size, N, is 450, and DF for that full model is 450-k-1. It looks like you have 6 independent variable coefficients (assuming any categorical variables are dichotomous and you’re fitting an intercept), and one intercept, so DF would be 450-6-1= 443.
Does the t subscript change at all? It’s possible the width of their cross-section was a span of several years (making it look or sound like a time series on the surface). They might even have a time series, but also have cross-sectional data and only use one at a time in different examples, but I can’t tell without more information.
Or 443 if 7 includes the intercept and only 1 dummy is needed for each of the categorical variables…either way, the way he just presented it, it doesn’t sound like this is a time series.
So if it’s 6 terms plus an intercept, you do N-6-1, but if it’s 7 terms and an intercept you do N-7-1; either way, DF isn’t 433 (could be an error for 4 4 3).
Does this help?
Yes it does, thank you very much. Also df is 443, sorry that was a typo on my end.
I’m glad it was helpful!