I am analyzing a panel dataset (n=1050, T=14) with individual effects modeled as fixed effects. The DV is a count variable. The DV and the independent variables (IVs) are non-stationary. After first differencing both the DV and the IVs, I have tested that they are all individually stationary (i.e., using xtunitroot in Stata to test for unit roots). My questions:

1) Do I need to conduct co-integration tests given that the individual series are stationary now (after differencing)? What's the benefit of the error correction model specifically? I have read that it gets at the long-run relationship but none of the books gave me a good example to help me decide if the short-run relationship is okay in my case.

2) Most of the books talking about the unit root tests and cointegration are focused on linear regressions. How do we do these tests with count variables?

  • $\begingroup$ Do you mind if I ask what are you counting? The reason I ask is that in some cases a non-stationary variable can map onto a stationary one and this eliminates the problems associated with the lack of stationarity. While I can think of strictly countable data that would be non-stationary, are you sure it is? Just because something tests as non-stationary does not mean it is non-stationary. The question you should ask is whether or not it is logically non-stationary. For example, is the count growing at an exponential rate? $\endgroup$ – Dave Harris Apr 10 '17 at 20:53
  • $\begingroup$ To give an example of what I mean, stock returns are non-stationary, but bankruptcy rates are stationary since they are bounded between 0 and 1. Because a non-stationary distribution is mapping onto a stationary one, it makes the overall process stationary. At least in theory, you can map any distribution onto any other by mapping the quantile function of one onto the other. Mapping to a stationary series makes the non-stationary series stationary through the mapping. $\endgroup$ – Dave Harris Apr 10 '17 at 20:58
  • $\begingroup$ I am looking at the number of daily submissions to contests (usually last for two weeks). Because people like to submit late, the daily submissions tend to go up as it gets closer to the end. This creates non-stationarity. I suppose I can just treat it as a continuous variable and carry out the panel data analysis but that is not ideal. $\endgroup$ – user2869951 Apr 11 '17 at 3:39

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