Control for Industry and lagged dependant variable

[Abi ayad]

Hello,
I'm doing my master thesis and I'm using a multitple linear regression. I'm regressing CSR performance of 2017 on CSR contracting and I'm controlling
for various control variables : CSR performance of 2016, ROA, Size, Leverage and R&D Intensity.
Controlling for Industries is also important according to the literrature and past studies have included the lagged dependant variable as an explanatory variable (CSR Performance 2016 is a control variable while CSR Performance 2017 is my dependant variable) so I simply followed them.
My question refers more to the intuitition behind those two concepts of controlling for industries and including a lag dependant variable.
I explain myself : If I understand well, controlling for industries allows me to control for industry fixed effects which are effects that are unobservable
and that varies between the different categories of industries. Is my intuition correct?
Also I'm controlling for the CSR performance of 2016 which corresponds to my dependant variable (CSR performance 2017) but one year before. and again
I'm not sure whether my intuition is correct or not. My intuition: controlling for CSR Performance 2016 allows me to control for observable and unobservable past information
for each firm. But one problem here is that I can't control for unobservable effects that varies accross time. Is my intuition correct again?

[Clyde Schechter]

If I understand well, controlling for industries allows me to control for industry fixed effects which are effects that are unobservable

and that varies between the different categories of industries. Is my intuition correct?

Yes, this is basically correct. It would be somewhat better to say it as adjusting for industry fixed effects adjusts for any attributes that are constant within any industry, whether observable or not.

My intuition: controlling for CSR Performance 2016 allows me to control for observable and unobservable past information for each firm.

No, All this does is adjust for the effects of the previous year's CSR performance, nothing more. Other attributes of the firm remain unadjusted in this analysis, even if those attributes do contribute to the firm's previous year CSR performance. The only attribute of the firm you are adjusting for here is the previous year's CSR performance, no more, no less.

But one problem here is that I can't control for unobservable effects that varies accross time. Is my intuition correct again?

Well, this is true. But there is an aspect of this question I don't understand. You don't say anything about having panel data here, and you don't say anything about an outcome for any year other than 2017. So there is no time variation in your data anyway--the closest you come to having time varying data is that one variable is a one year lag. So if that's the case, there are no time-varying forces operating in your data anyway.

[Abi ayad]

Thank you very much Clyde, it helped me a lot

[daniel klein]

[...] past studies have included the lagged dependant variable as an explanatory variable (CSR Performance 2016 is a control variable while CSR Performance 2017 is my dependant variable) so I simply followed them.
[...]
My intuition: controlling for CSR Performance 2016 allows me to control for observable and unobservable past information for each firm.

No, All this does is adjust for the effects of the previous year's CSR performance, nothing more. Other attributes of the firm remain unadjusted in this analysis, even if those attributes do contribute to the firm's previous year CSR performance.

While Clyde's explanation is basically correct, I would like to add a strong warning. One of the most important assumptions for unbiased coefficients in linear regression is that the error term(s) are not correlated with the predictors. The error captures any (unobservable) attributes that are omitted from the model but affect the outcome. Because the error affects the outcome at time t, it is very likely that it also affects the outcome at time t-1. If there are unobserved time-constant attributes, then these attributes will, by model definition, affect the outcome at any point in time. Therefore when you just plug in the lagged outcome/response/dependent variable as a predictor in a linear regression model, you will have, by model definition. introduced an endogeneity problem. By trying to adjust your estimates you will (sometimes badly) bias them. Do not get fooled by tons of articles (in my field at least) that do this; it is, in most cases, not statistically sound (see Halaby [2004, p. 536ff.]).

Best
Daniel


Halaby, C. N. 2004. Panel models in sociological research: Theory into practice. Annual Review of Sociology, 30, 507--544.