How to present economic significance for Probit and OLS results in Stata

[hussein bataineh]

hi

I am working on two regressions and would like to learn the proper way to present economic significance (not only statistical significance) for both models.

I would like to ask how to present economic significance in Stata using code for the following two models.

(1) Probit

 probit hard_final_Exact_new csopresence1 Firm_Size_w ROA_w Leverage_w Market_book_four_w ///
    Non_pension_CFO_w STD_CFO_w board_size_w female_percentage_w independent_percentage_w ///
    SUSTAIBILITY_COMTEE_FU Fund_Status_w FUNDING_RATIO_w Platn_Size_w i.year i.ff_12, robust cluster(id)

margins, dydx(*)

My understanding is that the marginal effects from margins, dydx(*) can be interpreted as the change in probability (in percentage points) associated with a one-unit change in each regressor, holding others constant.
Is this the correct way to interpret and report economic significance for a Probit model?


(2). OLS model

 reg csr_w hard_final_Exact_new csopresence1 Firm_Size_w ROA_w Leverage_w Market_book_four_w ///
    Non_pension_CFO_w STD_CFO_w board_size_w female_percentage_w independent_percentage_w ///
    SUSTAIBILITY_COMTEE_FU Fund_Status_w FUNDING_RATIO_w Platn_Size_w i.year i.ff_12, robust cluster(id)

For OLS, should economic significance be presented simply by interpreting the coefficient magnitudes, or is there a Stata command (e.g. margins, lincom, or beta) that can be used to compute and report economic significant ?

Any examples or best practices on how to code and present economic significance directly in Stata would be greatly appreciated.

[Felix Bittmann]

Economic significance is similar to practical significance, I guess. For OLS, you can look at measures of effect size, which is common to do in the field of psychology. After the reg command, type

estat esize

For more information see https://www.stata.com/manuals/resize...rksandexamples

This does not work for probit. I think the change in probability is a good way to tackle this. Maybe there are user-written packages to help you out, but I don't know them, if they exist.

[Carlo Lazzaro]

Hussein:
as an aside to Felix's helpful reply, please note that deciding whether a given set of results has practical significance or not, implies the knowledge of both the theory and the data generating process your research question refers to.

[Maarten Buis]

Effect size measures are basically some variation on standardized coefficient. They are important in psychology because many things they measure don't have a natural unit (It does not make sense to say "I am 6 kg happy"). Some form of standardization is necessary in those cases in order to get a unit. In economics many measures do have units, and than it is important not to standardize, because than you loose that unit. So the way to present economic significance is just to interpret the coefficient. In case of linear regression¹ no programming is needed, you can directly interpret the coefficients. With a probit, you can use margins as you suggested.

Alternatively, if all you are going to interpret is the average marginal effects, then you are basically estimating an approximation of a linear probability model. You don't need to approximate a linear probability model in two steps; you can directly estimate one in one step. It is easier to estimate, easier to communicate to your audience what you did (and its limitations), easier to diagnose, and you get the real coefficients you are looking for and not an approximation. It is completely beyond me why anyone would prefer probit followed by margins over a simple regress with the vce(robust) option (i.e. a linear probability model).

¹ Pedantic note: The correct way to refer to your model is linear regression, not OLS: In your case you care about the model, not the algorithm used to estimate the coefficients. Ordinary Least Squares is the algorithm used to compute the coefficients, linear regression is the model.