A test to choose between Tobit, Two Part Model, PPML and Fractional Logit.

[Imran Khan]

Dear all,

I am interested in investigating the influence of natural disaster related deaths on bilateral foreign aid allocation. In other words, I want to examine whether and to what extent donors allocate aid to recipient countries which have suffered from a natural disaster in time t. I have a three dimensional panel (recipient*donor*year). The dependent variable measures the share of aid received by a recipient from the total aid budget of the donor in a year. Since some recipients do not receive any aid from a particular donor, the dependent variable have lots of zero observations.

Given this nature of dataset, to the best of my understanding, I can’t use OLS due to following three reasons:
1) The censored nature of the data (non-negative values of DV).
2) Lots of zero observations.
3) DV measure the proportions of aid i.e., it is bounded to be in between 0 and 1.


The literature suggests to use the following estimators in this setting and for the following reasons:

Tobit
It will estimate the chance of censoring at the same time as estimating the amount of aid, if not censored.
However, assumptions need to be tested for the validity of estimator: 1) Errors are normally distributed, 2) The size and effect of the variables affecting which countries receive aid, and how much, should be same.

Cragg Two Part Model
The selection of aid recipients and aid allocation to the selected recipients can be estimated completely separately.
However, assumption need to be tested for the validity of estimator: Independence of the error terms.

Fractional Logit
It can estimate the fractional response variable in values between 0 and 1.

Poisson Pseudo Maximum Likelihood (PPML)
It outperforms Tobit in the presence of many zeros (Santos Silva and Tenreyro (2006 and 2011).


I have two questions in this regard:
Question 1: Is there any formal test in Stata to compare the models i.e., Tobit, Two Part model, Fractional Logit and PPML?
Question 2: Can I also use the same estimator if I want to measure the dependent variable in absolute amounts?


Best regards,
Imran Khan.

[John Mullahy]

Imran: While some specifications of the Cragg model (i.e. probit and truncated normal) nest a Tobit specification, for the most part the models you describe are non-nested. Testing against each other then would require a different strategy (e.g. cross-validation prediction-error magnitudes, etc. etc.).

However, Tobit, Cragg, and Poisson all expect outcomes in the [0,infinity) range, so I'm not sure any of these is well suited to a fractional measure in [0,1]. Fractional regression or its zero-inflated version would seem a more natural strategy here unless you wanted to analyze in "absolute amounts," in which case fractional regression won't be appropriate but the others might be. In that case you might also consider glm with a log link, a cousin of the PPML-Poisson approach.

So it seems to me the first issue for you to resolve is whether to estimate models of fractional or "absolute" outcomes. This is largely a conceptual consideration, not an econometric one. Once this is decided the range of econometric options narrows somewhat.

[Imran Khan]

Dear John,

Many thanks for your reply.
I have understood your point to some extent.

I am interested in estimating the model with DV in proportions i.e., the percentage share of the foreign aid received.
I am wondering if I could use fractional logit with fixed effects on a panel data?

Best regards,
Imran Khan.

[Joy Das]

what is the Stata code I can use for zero-inflated tobit model?