Fixed effects model with dependent variable that can only increase

Question

I am estimating the following the model:

$\Delta y_{ijt} = \alpha_{j}*\alpha_{t} + \beta*x_{it-1} + \epsilon_{ijt}$,

where $\alpha_{j}$ are individual dummies and $\alpha_{t}$ are time dummies, such that $\alpha_{j}*\alpha_{t}$ is a high-dimensional categorical variable (roughly 34000 dummies). $x_{it-1}$ are some other (continuous) controls, $\epsilon_{ijt}$ is the error term. $\Delta y_{ijt}$ is defined as $y_{ijt} - y_{ijt-1}$, whereas $y_{ijt} > 0 ~\forall ~i,j,t$ and is continuous. I estimate the model using OLS on the demeaned data (within-estimator rather than actually including the dummies).

By construction I have $y_{ijt} > y_{ijt-1} \Rightarrow \Delta y_{ijt} > 0$. Can this property of $\Delta y_{ijt}$ cause problems (biased estimates of coefficients, biased standard errors)? I got an remark suggesting this but haven't had the chance to asked the person who made the remark for further explanation. So, I'll hoped someone here can provide some clarification.

Answer 1

Strict positivity isn't a problem in general. Many real-world quantities are strictly positive and can be analyzed just fine with ordinary least squares, as long as your data fits the necessary assumptions, such as independence of samplings and (near) constant variance of residuals across all relevant subgroups.