I have tested the unit root for my panel data, some of the variables are stationary in first difference, and some of them in level, should I take any log for my variables? But the dependent variable is stationary at first difference.
It is not necessary to take log (or ln) of any variable. In some cases you can try using variables at level and variables with log then compare the performance of the models and choose the one with higher performance. Concerning that some variables are stationary at level and others are at first difference (Which is usually the case), it would be better to employ an ARDL model.
Since "log" is a monotonic transformation of the series, one should take log if the variable is in level and there is no negative value. Another advantage is that 1st difference of log transformed series indicates returns/growth rate
Better to use log (or ln) when the time series has positive (and non zero) values
There is no obligation to use log
Warning: log fot first difference is not a good choice.
The dependent variable being stationary at first difference means it is I(1), so there is no problem regressing the mix of I(0) and I(1) independent variables on I(1) dependent variable; you can simply use ARDL bounds test for cointegration on all the variables or take out all the I(1) variables and test for cointegration on them using Johansen technique. Log can be used in 2 instances, (i) when you need to interpret your results in percent changes or elasticities and (ii) to bring all variables to the same level (thereby getting rid of outliers in the process).
Hope the above helps.
if your variable are stationary I(1) then use johansen co-integration technique. but According to econometric theory if some variables are stationary at level and some are at first difference then ARDL bounds test for co-integration give you best result. in our case my variables are mix stationary that's why we use ARDL. I recommend my Article to you effect of Macroeconomic variables on stock market volatility.
@Muhammad Farhan Basheer, kindly see the link below
https://www.google.co.za/amp/s/www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/amp/
reduce heteroskedasticity and to normalised the data when you observe that the mean of the variable is greater than the median.Moreover the interpretation of an OLS model is based on the assumption of normality
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