Multivariate timeseries regression - use of a dummy variable between two time periods

#1
Dear stat people

I am doing an analysis on how the relation between Y and three explanatory variables change from one time period to the next. I guess using a dummy is an appropriate way to do this? I divide the time period into two subperiods, with monthly observation for 1990-2000 and 2000-2010.

Is the following regression statistically reliable to study the change in the relations?, D=Dummy variable = 1 for 2000-2010:

∆Y(i,t) = μ(i,t) + β1*∆X1(i,t) + β2*∆X2(i,t) + β3*∆X3(i,t) + D*β4*∆X1(i,t) + D*β5*∆X2(i,t) + D*β6*∆X3(i,t)+ ε(i,t)

I study the betas in the first period from b1, b2, b3. I will study the change in the relation to the second period with the sums of the betas for each factor: b1+b4, b2+b5, b3+b6. Also I study the joint significance of the second period sum betas with Wald test. Is this correct interpretation of the results?

Help much appreciated.
- dummy mouse