# Can I use a two-limit tobit model to drop certain outliers?

I am implementing a Tobit model, since my dependent variable (educational expenditure shares) is left-censored at 0. Below you'll find a swarmplot of the dependent variable and the explanatory variable of interest (gender specific bargaining power converted to dummies: 1 for male; 2 for female; 3 for mixed).

Aa you can see I have some large outliers I would like to drop. Naturally I can just identify them in my dataset and delete the observations. However, since I am using the Tobit model, which also allows for right-censoring (two-limit-Tobit model) I was wondering if I could just set the right-sided limit f.e at 0.35 and thereby drop the outliers? I thought about this: \begin{align} y_i = \begin{cases} y^*_i & \text{if } 0 < y^*_i < 0.35\\ 0 & \text{if } y^*_i \leq 0 \end{cases} \end{align} I have the feeling that this would have a different implication as I understood that the truncated Tobit model "drops" observations. Could I then truncate from above, censor from below? Or is this in general a bad idea?

• I wouldn't call your variable censored when it's just a question of natural bounds. Is number of children censored because there's a lower limit of 0? Is an indicator "owns car" censored because there are limits of 0 and 1? I'd use a logit link function here. For more discussion see e.g. ageconsearch.umn.edu/bitstream/122595/2/sjart_st0147.pdf (The outliers are just high values and unless you can show independently that they are incorrect you shouldn't want to omit them. There is likely to be an interesting and informative story there.) May 15, 2018 at 13:48
• stata-journal.com/sjpdf.html?articlenum=st0147 is a better link. Same paper at the time of writing, but less likely to be fragile. May 15, 2018 at 14:02
• Hi Nick! I thought that in this econometric problem regarding expenditures, zero observations represents corner solutions, such as that a consumer is either unwilling or not able at all to make a consumption choice. Thus Tobit is a good choice. Here is a paper, where the authors faced a similar problem an applied Tobit regression: ideas.repec.org/a/eee/wdevel/v38y2010i4p555-566.html Thank you for your advice though, I will make use of the logit link function and see if it produces sound results! Jun 6, 2018 at 13:49
• As I understand the question is whether in principle you can go lower than 0, and the answer to that appears to be No. I am not an economist or econometrician. Jun 6, 2018 at 14:05
• Sorry, still lost, as I don't know what "fact" you're referring to. Again, I suspect you're confusing logit link (as in Stata commands such as glm and xtgee) and logit transformation. No commands based on link functions create or change the data. Jun 23, 2018 at 15:05