I am doing panel data analysis. I have N= 103 firms in T= 5 years (that is around 507 observations with an “unbalance data” fixed effect). The study period is from 2008-2012. The period of the financial crisis is 2008.
I am not sure whether I can use a differences in differences model to get the effect of the crisis. I can’t see a control group because all companies were affected by the crisis.
Michael R. Roberts talks in his book "Endogeneity in Empirical Corporate Finance" about single time-series difference before and after treatment. Does he mean to interact my independent and moderating variables with a crisis dummy which is the year 2008? And is it right to interact the crisis dummy with all the observations to get the crisis effect?
Best Answer
If you have no control group, then you can't do Diff-in-Diff.
Since you are interested in estimating the effect of some other variable on an outcome and seeing whether the effect is different during and after the crisis, I think that you would want to run some regression like:
$y_{it} = \beta_0 + \beta_1 x_{it} + \beta_2 Crisis_t * x_{it} + \tau_t + c_i + \epsilon_{it}$
Here you are interested in the effect of $x_{it}$ on $y_{it}$ and if it is different during the crisis than it is after the crisis (this is equivalent to testing whether $\beta_2 = 0$. $Crisis_t$ is a dummy variable $=1$ in crisis years (2008) and $=0$ otherwise.
$\tau_t$ are dummy variables for each time period. These should soak up differences in outcomes related to the time period, and are probably important to include. $c_i$ are individual fixed effects.