Dear all,
I would like to investigate how a time-constant (by nature) variable affects the change of another variable from one wave to another (2 waves in total). Also, as the data is nested, I use multilevel modelling. I went with a first-difference estimator and generated the change of the dependent variable in a new variable, then using mixed to estimate the model. My question regards the nocons option. As regularly suggested, in these models, the nocons option should be used. I would like to ask how this option affects a ML model and if there is any guidance. I set up this toy example:

Code:
webuse nlswork, clear
keep if inlist(year, 71, 72)
keep if inlist(race, 1, 2)
keep year race hours ind_code idcode
reshape wide hours ind_code, i(idcode) j(year)
gen diff = hours72 - hours71

mixed diff i.race || ind_code71:   //assuming that industry is constant for the sake of the example
mixed diff i.race, nocons || ind_code71:

Given this example, I wonder which model is more appropriate. I tested both with my own data and see only little difference for the vars of interest. However, what I do notice is that in the nocons model, the random the RE sd(_cons) of the cluster level increases drastically (from about 0.20 to 1.1). Thanks for any comments on the topic.

References:
https://www.statalist.org/forums/for...nce-regression
https://www.stata.com/statalist/arch.../msg01258.html