Censored and truncated models
Tobit regression
Censored expenditure model.
The task
Task statement
The observed expenditure y is left censored at zero. Fit a homoskedastic Gaussian Tobit model for latent y using an intercept, x, and z. Include every row, including observations with y=0. Use maximum likelihood with lower censoring point 0 and no upper censoring. Report latent-equation coefficients const, x, and z with conventional observed-information standard errors from the jointly estimated likelihood. Report sigma, the standard deviation of the latent Gaussian disturbance, with se=null. Report the full sample size as n_obs for every row.
Data
One shared fixed dataset with 400 rows. Columns: id, y, x, z.
- Files
- input.csv
Required output
Scored estimates: const, x, z, sigma.
Reference output
| Term | Reference estimate | Sample size |
|---|---|---|
const | 0.20029164 | 400 |
x | 0.8350899 | 400 |
z | -0.65088889 | 400 |
sigma | 1.0896912 | 400 |
A run succeeds when every scored estimate lies within 1 percent or 0.005 of its reference value, whichever is larger. Sample sizes are not scored.
Task success
| Agency condition | Claude Sonnet 4.6 | GPT-5.6 Luna |
|---|---|---|
| Chatbot | 81.7% | 80.0% |
| Self-repair | 88.3% | 93.3% |
| Constrained agent | 100.0% | 98.3% |
- All runs
- 90.3% of 360 runs
- By prompt condition
- Zero-shot 82.2%, One-shot 98.3%
- By software
- Python 98.3%, R 98.3%, Stata 74.2%
About this benchmark task
- Method group
- Censored and truncated models
- Software
- Stata, R, and Python
- Runs
- 360 runs, ten in each combination of model, software, prompt, and agency condition