Help on Writing out Regression Equation for Panel Data inc. Industry and Time Dummies

[sophie chow]

Hello,

I'm trying to write out my regression equation inc. industry and time dummies, but I'm not sure whether I've written it out correctly - could I get some help please?

For the industry and time dummies, is it mean to be written out like that? I know I have to write out a dummy coefficient before industryi and for yeart, but I am not sure if it's meant to be diindustryi

[Carlo Lazzaro]

Sophie:
welcome to this forum.
As your regressand is continuous, please get yourself familiar with the example reported in -xtreg- (for panel data regression) and -fvvarlist- (for creating categorical variables and interactions in a really fruitful way).

[River Huang]

Dear Sophie, There are many ways to do this. A simple one is something like

reg y x1 x2 ... i.industry i.year, robust

[sophie chow]

Hello,

Thank you for your replies - I was actually wondering if I had written the time and industry dummies out correctly in the equation, not how I would do it on stata

Thanks,

Sophie

[Andrew Musau]

It is not clear whether your observations are at the firm level or at the industry level, and that is why presenting your regression command is useful. Clearly, your expression in #1 is incorrect because with \(J\) industries, you will have \(J-1\) industry dummies and \(T-1\) time dummies, and this is not reflected in your equation. Secondly, \(u_{i}\) represent the unit fixed effects, and if these are firms, they will be collinear with the industry dummies (unless firms change industries which is usually not the case). On the other hand, if these are industries, they are identical to the industry dummies and you have to choose one representation. Assuming that your observations are at the firm level and you run the following OLS regression,

regress lny L.lnx1 L.lnx2 L.lnx3 i.industry i.year, cluster(firm)

you can write this as

$$ln y_{it}= \beta_{0} + \beta_{1}lnx1_{it-1} +\beta_{2}lnx2_{it-1}+ \beta_{3}lnx3_{it-1}+\gamma_{2}industry2_{j}+\cdots+\gamma_{J}indust ryJ_{j}+\delta_{2}time2_{t}+\cdots+ \delta_{T}timeT_{t}+e_{it}$$

where \(i\) indexes firms, \(i=1,\cdots, N\), \(j\) indexes industries, \(j=1,\cdots, J\), and \(t\) indexes time, \(t=1,\cdots T\).

[sophie chow]

this is the regression command

regress logroe lagproportionfdirectors laglogfirmsize lagnodirectors i.industrytype2 i.year, cluster(coid)