Right model when dealing with lots of zeros in DV

[Tim Huizingh]

Dear community,

I am working with an ESG index score as DV. This variable can range from 0 (minimum) to 1 (maximum). Now, I wonder if using MLR is the right approach since 291 out of the 412 observations have a value of 0.
The index is dispersed as follows:

Total ESG |
Score | Freq. Percent Cum.
------------+-----------------------------------
0 | 291 70.63 70.63
.1111111 | 10 2.43 73.06
.125 | 46 11.17 84.22
.2 | 3 0.73 84.95
.2222222 | 9 2.18 87.14
.25 | 29 7.04 94.17
.3333333 | 5 1.21 95.39
.375 | 13 3.16 98.54
.4444444 | 2 0.49 99.03
.5 | 2 0.49 99.51
.75 | 2 0.49 100.00
------------+-----------------------------------
Total | 412 100.00

I am considering using a Two-Part Model with OLS for the second part, but I was wondering whether this is the right approach or if I should use a different model.

I appreciate any help you can provide.

[Erik Ruzek]

I would use a two-part model with an outcome such as this. There's a nice Stata blog post on how to use gsem + margins to get quantities of interest.

[Jeff Wooldridge]

With an upper bound of one, a linear model for the second part doesn't make a lot of sense. You can avoid to TPM by just using fractional logit as in Papke and Wooldridge (1996, Journal of Applied Econometrics). Because you don't see one ones, you can use a TPM based on fractional logit. First, model the zero versus positive outcome via logit. Then, conditional on y > 0, use fractional logit. Both are easy.

But I would start with linear regression then try fracreg, without the complication of a TPM. The partial effects are harder for a TPM.

I just checked, and this appears in Problem 18.8 in my 2010 MIT Press book on cross section and panel data analysis.