I have trade in goods (% of GDP) and trade in services (% of GDP) as explanatory variables then does it sounds good if I take log of them to include in my model since its already in percentage? Also, please guide whether including both trade in goods (% of GDP) and trade in services (% of GDP) together in a single model will cause multicollinearity problem? Please guide.
Thanks
1. Its OK to use log.
2. Depends on the econometric technique used to analyse the relationship.
USE OF LOG: Log is used for scale invariance in self-similarity cases. For example, a large number may be made small, i.e. log(1000) = 3 for log based 10. In case of natural log base e, ln(1000) = 6-.9077. in you case, the actual value (which is measure in hundreds of millions, is not use but its % of the GDP, this number is already small. If you want to convert to a large scale, you could just multiple the % by the GDP and you will get back the actual volume: in millions of dollars.
COLLINEARITY: The predictors (X1, X2, ...) are called "independent" because we require then to be independent from Y (dependent variable) and from other predictors on the right side of the equation:
(1) Y = B0 + B1X1 + B2X2 + e
If X1 and X2 correlates, the value of Y would be inflated leading to non-rejection of null hypothesis: Type 2 error.
LATENT EFFECT: If you are looking for the latent effects among X1 and X2 and how the interaction between X1 and X2 produces Y, then collinearity could be a useful study in and of itself. In this case, equation 91) is modified, thus:
(2) Y = B0 + B1X1 + B2X2 + B3X1X2 + e
Here, the quantity B3X1X2 measurs the moderation of the independent variables in the model. The determination of B3 is given by:
(3) B3 = B^ -B1 - B2 - B0
(4) B^ = Y* - (B2 - B0) - B1 where Y* = mean of the response variable Y. The test statistic is given by:
(5) T = (B1 - B2) / sqrt(A /C)
(5.1) A = n1SE12 + n2SE22
(5.2) C = n1 - n2 - 2
Whereas the general caution of collinearity is that it may lead to inflated response value, and thus leading to inferential error. However, if carefully modeled and monitored, it could provide useful information.
REFERENCES: See attached articles.
http://en.wikipedia.org/wiki/Multicollinearity
http://en.wikipedia.org/wiki/Natural_logarithm
It will not change anything I guess. Taking logs, just reduces the magnitude of data in relation to other variables data, and the properties of the model are not lost in any case. What is crucial is to know why you are taking the logs? is it that data have too big magnitudes or its for easiness of variable coefficient analysis. Taking logs will not change anything.
I generally leave percents in levels as the beta coefficients are more meaningful to percent change in percents that would be estimated in logs.
Yes I agree with "USE OF LOG: Log is used for scale invariance in self-similarity cases. For example, a large number may be made small, i.e. log(1000) = 3 for log based 10. In case of natural log base e, ln(1000) = 6-.9077. in you case, the actual value (which is measure in hundreds of millions, is not use but its % of the GDP, this number is already small. If you want to convert to a large scale, USE OF LOG: Log is used for scale invariance in self-similarity cases. For example, a large number may be made small, i.e. log(1000) = 3 for log based 10. In case of natural log base e, ln(1000) = 6-.9077. in you case, the actual value (which is measure in hundreds of millions, is not use but its % of the GDP, this number is already small. If you want to convert to a large scale, you could just multiple the % by the GDP and you will get back the actual volume: in millions of dollars.
Why dont multiple the % by the GDP and you will get back the actual volume: in monetary units
Log transformation is necessary to make data in smaller scale to reduce non-linearity. In other way, to make data more linear for making estimators BLUE. If data are in percentage form, log transformation is absolutely not necessary.
Taking log of a dependent variable and a covariate ,apart from reducing scale when useful, has also the effect in OLS that you can intepret the estimated coefficient as an elasticity: this is no more the natural interpretation of elasticity if you take the log of a percentage share as in your example. You would be saying that a x% change of the %share relates to a %change of the estimated variable. A bit messy. Moreover, the output is good+services , you cannot take the two shares at the same time as they are perfect complements (if you use goods and services in the usual meaning)
PLZ answer in YES or NO
Can we take log of percentage shares i.e assets(as% of GDP)?
Most of the cases it is not right to take log of any interest rate series or growth rate series which is I(1) series.
Because if we take log and then first difference of that series , that implies, logx(t)-logx(t-1) approximates to x(t)-x(t-1)/x(t-1) that means we are taking growth of growth or growth of interest rate
what determines if you are to take log or not is your model specification. if is log linear model, all the variables must be in log. if is semi-log model, not all.
There is an interesting inquiry on this issue in the following paper of Christer Gerde's
Christer Gerdes, 2011. "Using “shares” vs. “log of shares” in fixed-effect estimations," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 54(1), pages 1-7.
This could make absolutely sense...
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