Help with interpretation of coefficients in a diff-in-diff regression

[Mathieu Terster]

Dear All,

I am researching if companies with high and low market-to-book ratios have different investment ratios between rated and non-rated firms. Therefore, I performed the following regression where highmb is a dummy which takes 1 if the firm has a high market to book ratio (>1) and 0 otherwise, and where rated is a dummy which takes 1 if the firm is rated and 0 otherwise and where interaction is highmb*rated. I performed the following regression:

regress inv_k highmb rated interaction, robust

Linear regression Number of obs = 4,452
F(3, 4448) = 19.15
Prob > F = 0.0000
R-squared = 0.0040
Root MSE = 8.1674

------------------------------------------------------------------------------
| Robust
inv_k | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
highmb | 1.154348 .1813159 6.37 0.000 .7988786 1.509817
rated | -.0860253 .0389997 -2.21 0.027 -.1624841 -.0095665
interaction | -.9007188 .1917744 -4.70 0.000 -1.276692 -.5247456
_cons | .2426598 .0186916 12.98 0.000 .2060149 .2793046
------------------------------------------------------------------------------

Could you help me interpret each coefficient and find the average investment ratio (inv_k) for each of the four combinations of rated and market to book dummies? In addition, how can I double-check my results by computing sample averages for each of the subsamples? And how can I check if investment for high/low market to book ratios differ for rated and unrated firms?
Please help me with the Stata commands.

Thank you in advance for your answers.

Best regards

[Carlo Lazzaro]

Mathieu:
welcome to the list.
Two remarks about your query:
- why creating interactions yourself when -fvvarlist- can do it for you, paving the way to two wonderful post estimation commands such as -margins- and -marginsplot- (see related helpfiles)?
In your case, the regression equation can be written more efficiently:

regress inv_k i.highmb##i.rated, baselevels

The -baselevels- estimation option will help you out in understanding the output of the interaction as well as the one of the main conditional effect of the two interacted predictors;
- for the future, please post what you typed and what Stata gave you back via CODE delimiters (as advised in FAQ). Thanks.

[Clyde Schechter]

Carlo's advice is an excellent first step. Once you have done that, you are ready to run:

margins highmb#rated

This will give you the expected inv_k in each of the four groups as output.

For determining whether inv_k for high and low book market firms differ for rated and unrated firms, that difference is estimated by the coefficient of highmb#rated 1 1 in your regression output and you can read out the confidence interval for that difference, along with its standard error, and, if you must, the p-value from that row.

[Mathieu Terster]

It is indeed a lot easier with the fvvarlist rather than creating an interaction variable... Thank you for your help!!