Dear Kapoor

You can not take the 1st difference of dummy variable, since it all becomes zero when you take difference

Best

Canh

Thank you so much. 

Actually I am trying to look at a normal time series regression. All the variables are not stationary and my main independent variable is a time dummy. How should I proceed

Dear Friend

I guess that you use time dummy variable to test the structure break if time series

=> in this case, I suggest you use the TVAR or STAR to estimate it

Cheers

Canh

The equation is almost like this.

Y(t) = bD +b1x1(t) + b2x2(t) 

Where d is the dummy that capture the impact of a policy on price. Can VAR OR STAR be used then as there are no lagged variables

dear Friend

Until this time, you are trying to test the impacts of a policy such as rising policy on price at specific date.

In this case, i suggest that you use the event study instead of time series model.

For instance, the central bank raises their policy rate 10 times in a year, you might want to test whether this change effects on price.

You might want to see this link

http://www.sciencedirect.com/science/article/pii/S0304393204001138

http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1997.tb04816.x/full

Cheers

Canh

Thank you so much. :)

You can always difference a dummy variable. What it looks like will depend on whether it is a 'step' [ 0 0 0 1 1 1 ] or 'pulse' [ 0 0 0 1 0 0] dummy variable. When you difference a 'step' dummy variable it actually becomes a pulse dummy variable, whereas when you difference a pulse dummy it becomes positive/negative [0 0 0 1 -1 0 0]. 

Can you suggest me any papers how to interpret it. My dummy variable is a step dummy variable.

Since it is a step dummy , there is no need differencing it .you already know that answer zero. How about differential intercept and differential slope?

HI, I have the same problem now. could you please teach me how to solve it? Thanks