I currently have a panel data set that contains the quarterly increment of loans initiated from more than 300 cities in China over the period from 2011Q1 to 2020Q2. I want to examine the impact of COVID-19 on lending activities. I believe that both time fixed effects and city fixed effects exist—both the F test for poolability and Hausman Test support a fixed-effect model.
I use the panel procedure of SAS to analyze it. I also set a dummy variable, "event", to indicate whether the pandemic has occurred. The dummy variable "event" equals to 1 if the period is 2020Q1 or 2020Q2. Currently, I have not added any interactive terms. If I specify a one-way model using fixone option that only allows cross-section fixed effects, I found that some coefficients of these fixed effects are significant while some are not. The coefficients of the dummy variable "event" and other control variables are also significant. By now, it is acceptable.
However, if I specify a one-way fixed effects model using fixonetime option that only allows time fixed effects, it will be a mess. Although the coefficients of all time fixed effects are significant, the coefficient of the dummy variable "event" becomes zero. I am wondering whether it is caused by perfect multicollinearity. After all, in my setting, event = 1 means the same thing as the fixed effects of 2020Q1 and 2020Q2. My guess is that the impact of the dummy variable "event" has already been absorbed by time fixed effects. Is that right? If it is correct, does it mean that you can never use the time fixed effects and some dummy variables indicating certain event happens at the same time? However, several papers are studying the impact of COVID-19 using them simultaneously in their model. They did not mention any problems of such a setting. So I feel confused.
In a branched setting, instead of using the dummy variable "event", I use two dummy variables, "event_level1" and "event_level2", which equals to 1 if the period is 2020Q1 and 2020Q2 respectively, to visualize the dynamics of COVID-19 impact. The result is getting worse because the coefficients of all fixed effects and interested dummy variables "event_level1" and "event_level2" become zero this time. It looks caused by other reasons instead of multicollinearity this time. Are there any generous and smart friends who know the reason? Thank you so much!