Stock return - Regression with multiple dummies I have a case where I want to test if a corporate credit rating change by Moody's affects the company/security that experience the event. I also want to test if the effect is more or less extreme after a specific financial regulation. Thus far I have set it up like this (where change is 1 when there is a credit rating change, regulation is 1 after the financial regulation and DID is the difference in differences):
| company_ID | stock_return | market_return | dummy_change | dummy_regulation | dummy_DID |
|-----------:|-------------:|--------------:|-------------:|-----------------:|----------:|
|          1 |        0.041 |         0.027 |            1 |                0 |         0 |
|          1 |       -0.027 |         0.012 |            0 |                0 |         0 |
|            |          ... |           ... |          ... |              ... |       ... |
|         34 |       -0.021 |         0.011 |            1 |                1 |         1 |
|         34 |        0.017 |        -0.012 |            0 |                1 |         0 |

And then regressed it:
$$R_{t}=\alpha _{} + \beta _{}R_{mt} + \gamma _{}D_{change} + \delta _{}D_{regulation} +  \lambda _{}D_{DID} + u_{t} $$
where $\beta$ is the exposure to the market (around 1 if every stock is included), and $\gamma$, $\delta$ and $\lambda$ are the return associated with changes in credit rating, financial regulation and the difference between a change before and after the financial regulation.
This was my thought. However, I'm not sure if this method is either meaningful or appropriate. Can we state that a significant value of say $\lambda$, is proof that there is a difference before and after regulation? 
 A: Interesting question. The bottom line is that there is more than one way to specify a model and unless you have a PhD committee scrutinizing your work, you have a lot of leeway to motivate a wide range of approaches.
You are right to control for market returns but what about additional control variables for sector or industry? This would be logical in that regulatory changes can have widely differing impacts by industry. It would also offer the option to consider a multi-level approach to modeling since stocks (entities) are nested within industry.
Rating changes can be both up and down, correct? I question using a single 0,1 dummy variable to capture these changes. A better approach would be to use effect size coding where -1 is a downgrade, zero is no change and +1 is an upgrade. However, both of these approaches to coding won't capture differential effects as a function of the level of the rating. In other words, if you plugged in the actual rating grade (e.g., Aaa, Ba1, etc.) and tracked the rating changes this way, your model would be sensitized to the level of the rating and, therefore, more informative. 
Similarly, regulatory changes are usually not just of a single type and using one 0,1 dummy variable to capture them will collapse any nuances in the regulatory changes into a single effect that will not be further decomposable. You might consider the possibility of integrating additional classifications to the regulatory change variable.
The beauty of the pooled time-series model you've proposed is its simplicity and flexibility. Regrettably, market returns are also known to be sensitive to autocorrelation, periodicities, trends and seasonalities of various types such as day of week, week and month of year, etc., some of which can only be assumed away under pooling. If you have enough data points, you can control for these issues as well, further refining your estimates. This would necessitate shifting the functional form from the pooled, MNL approach you're leveraging now to a more HAC (white noise residual) ARIMA or GARCH-type model where lags, MVAs and/or variance regimes can be integrated, investigated and controlled for.
I'm confused by your DID factor. How are you specifying it? Would an interaction between the rating grade and regulatory changes be a simpler, more efficient and informative approach? 
Finally, does the temporal range of your returns include 2008 crash days where returns might be extreme valued? If so, you might want to consider using quantile regression for more robust estimation.
Anyway, those are a few quick thoughts.
