Hi,
I may not be using the correct terminology in saying "second-difference", because I do not mean a difference-in-difference test. So, in other words, I am wondering under what conditions it is justified and advisable to use t-2 as opposed to t-1 in a "first-difference" test.
First, I have time series-cross sectional data (i.e., xt), in which N=53 and T=134, which is highly unbalanced (but due to different start and end dates, such as attrition, as opposed to gaps). I have already determined that an FD test is preferable to FE for several reasons. First and foremost, because of heteroskedasticity, serial autocorrelation, and non-normality. But, also due to the attrition, as well as the shape of my data (relatively large N with even larger T).
However, it is also worth noting at this point that this xt analysis primarly serves as a robustness check of the results of a time-series analysis, in which my N's are pooled together. For more background, this is an analysis of social media network data. So, in the primary time-series analysis, I am treating the entire network as a whole, and I am testing for the relationship between my IVs and DVs over time. (My time unit is weeks.) But, I want to conduct a robustness check of my time-series analysis by also testing the relationship at the "panel" level, by treating the specific nodes in my network as units (N)--hence the time-series cross-sectional analysis.
The primary time-series analysis identified an optimal lag of 2. And, the results of VAR, Granger causality, and IRF tests all show a significant effect of variables lagged at 2 weeks. This being the case, is there any reason or justification to calculate the FD test of the xt data as t-2, rather than the standard t-1?
Both show similar results, but the relationships are slightly more signficant at t-2. The results of the t-2 FD test also more closely "mirror" the results of the primary time-series analysis, which makes intuitive sense. (Since all of those results demonstrated significant relationship at a lag of 2.)
I have not found a lot of content online discussing the implications, limitations, and/or requirements of using t-2 vs t-1 for a FD test. And, I was hoping someone here might have some insight or be able to point me in the correct direction?
Thanks in advance!
I may not be using the correct terminology in saying "second-difference", because I do not mean a difference-in-difference test. So, in other words, I am wondering under what conditions it is justified and advisable to use t-2 as opposed to t-1 in a "first-difference" test.
First, I have time series-cross sectional data (i.e., xt), in which N=53 and T=134, which is highly unbalanced (but due to different start and end dates, such as attrition, as opposed to gaps). I have already determined that an FD test is preferable to FE for several reasons. First and foremost, because of heteroskedasticity, serial autocorrelation, and non-normality. But, also due to the attrition, as well as the shape of my data (relatively large N with even larger T).
However, it is also worth noting at this point that this xt analysis primarly serves as a robustness check of the results of a time-series analysis, in which my N's are pooled together. For more background, this is an analysis of social media network data. So, in the primary time-series analysis, I am treating the entire network as a whole, and I am testing for the relationship between my IVs and DVs over time. (My time unit is weeks.) But, I want to conduct a robustness check of my time-series analysis by also testing the relationship at the "panel" level, by treating the specific nodes in my network as units (N)--hence the time-series cross-sectional analysis.
The primary time-series analysis identified an optimal lag of 2. And, the results of VAR, Granger causality, and IRF tests all show a significant effect of variables lagged at 2 weeks. This being the case, is there any reason or justification to calculate the FD test of the xt data as t-2, rather than the standard t-1?
Both show similar results, but the relationships are slightly more signficant at t-2. The results of the t-2 FD test also more closely "mirror" the results of the primary time-series analysis, which makes intuitive sense. (Since all of those results demonstrated significant relationship at a lag of 2.)
I have not found a lot of content online discussing the implications, limitations, and/or requirements of using t-2 vs t-1 for a FD test. And, I was hoping someone here might have some insight or be able to point me in the correct direction?
Thanks in advance!
