# Right way to use lags?

I came across a study that analyzes firm performance. Specifically, it aims at answering the question if firing a CEO leads to better performance. In the study, the author splits the sample into two subsamples. Sample 1 has all firms that did not fire the CEO, sample 2 has only firms that fired a ceo and the firm performance 2 years after. The specification of the model remains the same for both samples. Means were compared.

This setup does not take advantage of the possible panel structure the entire sample provides. I wonder, if it would make more sense to fit the following model.

$$y_{it} = \alpha_i + \beta_1I(CEO_{it})+\beta X'_{it}+\epsilon_{it}$$ with $\epsilon_{it}\sim IID(0;\sigma^{2}_{\epsilon})$

where $y_{it}$ depicts the firm's performance, $I(CEO_{it})$ is a dummy and 1 if the firm fired a CEO in the period $t$ and 0 otherwise, and $X'_{it}$ is a vector of other covariates. This would in turn allow to use a lag structure:

$$y_{it} = \alpha_i + \beta_1I(CEO_{i,t-k})+\beta X'_{it}+\epsilon_{it}$$ with $\epsilon_{it}\sim IID(0;\sigma^{2}_{\epsilon})$

where $k$ indicates the desired lag-structure. Such as

$$y_{it} = \alpha_i + \beta_1I(CEO_{i,t-2})+\beta X'_{it}+\epsilon_{it}$$ with $\epsilon_{it}\sim IID(0;\sigma^{2}_{\epsilon})$ for $k=2$

I have two questions:

1. Can I exploit the panel structure in the way depicted?
2. Can I use the lag-structure in the way shown and intepret it as the influence of a CEO change $k$ periods ago on current performance?
• I don't quite get your comment. As far as I am concerned, dynamic merely implies a laged endogenous variable. Isn't sort of common to only lag a covariate and leave the endogenous variable as it is? Dec 17, 2015 at 14:09

You can use Indicator variable to model instead of the stratification approach. However, here you are trying to address another problem of trying to find the relationship of firing a CEO $x$ years ago to company performance. You may have to do an F-test to compare between models and change value of k to find the optimal lag. This is just one of the approaches. Else you can use a distributed lags approach to find the optimal lag of firing a CEO and company performance.