Threshold models for cross-sectional data

[Denila Jinny]

Hi,

I am working on cross-sectional data of firms. I am looking to study at what firm size (threshold) does a variable's influence cease to exist. I would like someone to point me in a right direction as to what kind of models should I look at. My data has a lot of categorical variables and few continuous variables. Any help is greatly appreciated.

[Charlie Joyez]

Hello Denila,

We would need a little more information about your objective : what is precisely the variable you want to check its influence and over which one. Are they continuous or categorical variables?
Concerning the firm size also, is this a continual variable (e.g. number of employees or turnover) or a categorical variable ("Small" ,"Big", etc...). This information could change the approach chosen.

Globally speaking, it seems like you want to check an interaction assumption, so you could try to interact the firm size variable with the one you want to check its influence. It would be even easier if the firm size is categorical (see help fvvarlist for details and examples).
But once again it depends on the shape of your data, and moreover your research question we don't know, many alternative are possible (sub-samples, interval regression, etc,.)

Best,
Charlie

[Denila Jinny]

Hi Joyez,

I measure size using asset value, and is therefore a continuous variable. I study capital structure's (categorical variable) impact on firm performance. I have evidence that this impact diminishes over size, This I identified using sub-samples. Now what I am interested in is the exact point at which this influence starts diminishing and/or becomes insignificant. I know I can make more sub-samples and reach closer to desired ends. I would like to know if there are better ways to do this. Please let me know if this is still unclear.

[River Huang]

1. As suggested by Charlie, an interaction model will do. Consider the following simple specification: $firm\_performance=\alpha+\beta_1 cs+\beta_2 size+\beta_3 cs*size+\epsilon$. By taking partial derivative with respect to size (and set to zero), you can the critical value for cs (capital structure) to have no effect on firm performance.
2. Consider the threshold regression of Hansen (2000), "Sample splitting and threshold estimation." Econometrica, 68(3), 575-603.