Estimating Latent Variable Models When the Latent Variable is Observable

Logit and probit models are designed to estimate latent variable models. However, there are cases that these estimates are used, even though the latent variable is fully observable. The most prominent examples are studies about obesity, where they calculate BMI based on two observed variables: weight and height squared. They translate BMI into a binary variable (e.g. obese or not obese) and this index is used to examine factors affecting obesity. This study determines the loss in efficiency of using logit/probit models versus the conventional OLS (e.g. with unknown variance). We also compare the marginal effects between these models. The results suggest that OLS is a more efficient than the logit/probit models when estimating the true coefficients, regardless of the multicollinearity, fit of regression and cut-off probability. Likewise, OLS provided unbiased marginal effects compared to both binary response models. It is also less likely to be biased. We can conclude, that according to our Monte Carlo simulation, when the latent variable is observable, it is better to use the continous value and regress it with respect to their explanatory variable instead of converting it into a latent variable.