Multivariate tobit model

[Jake McCollum]

Hi,

I am trying to run a multivariate tobit model using lots of dummy independent variables for my undergraduate dissertation. The mvtobit help file says "A limitation is that only models left ccensored at zero can be estimated". Is this to say that right censoring is not possible at all? My dependent variables are right censored. I have tried to use the cmp command as an alternative but it fails to converge the full model, returning hundreds of "logpseudoliklihood=0 (not concave) iterations. I believe this is due to multicollinearity. Is there a way to address this? Many thanks,

Jake

[FernandoRios]

Hi Jake
There is not enough information in your question to provide better advice, other than general guidelines.
1. Are you use you need a Multivariate Tobit? How many simultaneous Tobits are you interested in analyzing? And what is the structure of the dependent variables (what are they measuring?)
2. Make sure you understand what exactly the Tobit model does, and further, what are the assumptions for a multivariate Tobit. Otherwise, you are just blindly using a method without knowing what it will provide you as an answer.
3. The "limitation" you find is unique to -mvtobit- since that is how the author decided to program it. So Right Censoring is not possible with this command unless you "modify" your dependent variable. For example, by flipping the variable. Say new_x= - x. if "x" is right censored at 0, "new_x" will be left-censored at 0.
4. For -cmp-, you really need to set up the syntax correctly. I myself have had difficulties setting simple bivariate tobits, the reason for which I have written my own commands for that scenario.
5. Using Multiple dummies (how many are you trying to include) may be the problem, as you diagnose. So try a simpler model first, before attempting more complicated ones.
6. Unless you have strong reasons why you need a MVtobit, you can also use -suest- with simple univariate tobits. That may be more feasible, and easier to diagnose if you encounter problems of convergence.

HTH
Fernando

[Jake McCollum]

Hi Fernando,

Thanks for your advice. I have gathered survey data and am analysing the effects of the use of paid and free streaming services on attendance to different types of live music. I have 4 dependent variables: INTER_LIVE (concerts by mainstream artists); LOCAL_LIVE (concerts by less established artists); CLASSICAL_LIVE (concerts by classical artists); FESTIVALS (summer music festivals). My data for INTER_LIVE, LOCAL_LIVE and CLASSICAL_LIVE are right censored at 5, whilst FESTIVALS is not censored.

If you want to have a look, my analysis is very similar to that carried out by Moreau, Dejean et al (2014) in the paper "On the complementarity between online and offline music consumption: the case of free streaming". In this paper, they perform a multivariate tobit model on similar dependent variables. They suggest a mixed process recursive model as advocated by Roodman (2009).

My independent variables include socioeconomic variables (age, education etc), streaming usage and social media usage. I also include variables for music taste to control for endogeneity of "liking music". All of these are dummy variables besides SOCIALMEDIA.

I originally performed an individual OLS regression on festivals and a multivariate tobit regression on the other three dependent variables (following the precendent set by Moreau et al) before realising the mvtobit command works for data left censored at 0 only. I then began exploring the cmp function. Since my last post, I have managed to get STATA to produce suitable looking output using the following code:

cmp setup
cmp (FESTIVALS = MALE AGE24 AGE39 AGE59 EDUCATION1 EDUCATION2 INCOME1 INCOME2 INCOME3 URBAN RURAL SOCIALMEDIA RECOM_FRIENDS RECOM_INTERNET RADIO TV MUSICTASTE1 MUSICTASTE2 MUSICTASTE3 MUSICTASTE4 MUSICGROUP PAIDSTREAMING FREESTREAMING)(INTER_LIVE = MALE AGE24 AGE39 AGE59 EDUCATION1 EDUCATION2 INCOME1 INCOME2 INCOME3 URBAN RURAL SOCIALMEDIA RECOM_FRIENDS RECOM_INTERNET RADIO TV MUSICTASTE1 MUSICTASTE2 MUSICTASTE3 MUSICTASTE4 MUSICGROUP PAIDSTREAMING FREESTREAMING) (LOCAL_LIVE = MALE AGE24 AGE39 AGE59 EDUCATION1 EDUCATION2 INCOME1 INCOME2 INCOME3 URBAN RURAL SOCIALMEDIA RECOM_FRIENDS RECOM_INTERNET RADIO TV MUSICTASTE1 MUSICTASTE2 MUSICTASTE3 MUSICTASTE4 MUSICGROUP PAIDSTREAMING FREESTREAMING)(CLASSICAL_LIVE = MALE AGE24 AGE39 AGE59 EDUCATION1 EDUCATION2 INCOME1 INCOME2 INCOME3 URBAN RURAL SOCIALMEDIA RECOM_FRIENDS RECOM_INTERNET RADIO TV MUSICTASTE1 MUSICTASTE2 MUSICTASTE3 MUSICTASTE4 MUSICGROUP PAIDSTREAMING FREESTREAMING), indicators($cmp_cont "cond(INTER_LIVE>5, $cmp_right, $cmp_cont)" "cond(LOCAL_LIVE>5, $cmp_right, $cmp_cont)" "cond(CLASSICAL_LIVE>5, $cmp_right, $cmp_cont)") difficult robust
estimates table, star(.1 .05 .01)


Is it appropriate to include censored and non censored dependent variables in this function? Furthermore, the help file suggests that "Broadly, cmp is appropriate for two types of models: 1) those in which a truly recursive data-generating process is posited and 2) those in which there is simultaneity but instruments allow the construction of a recursive set of equations, as in two-stage least squares, that can be used to consistently estimate structural parameters in the final stage."

Does my model appear to fulfil these requirements? I do not use an instrumental variable to deal with endogeneity as in Moreau et al (2014) and am not entirely sure what "recursive" means in this context.

[FernandoRios]

In principle, yes. You can always mix and match censored, noncensored, and truncated data. It is harder to track down and estimate, but CMP does it for you.
So I think your model is fine, in terms of the mechanics.
The idea of recursivity here is when one is trying to estimate a model where some variables are endogenous, in which case instruments are needed. Or at least that is what I believe.
Best

[Jake McCollum]

Ok thank you. So, given I have used proxy variables to deal with enodogeneity rather than instrumental variables, is it fine for me to use the cmp function?