You are essentially dealing with a zero–inflated regressor problem: most regions (376 out of 400) have zero cement production, while only 24 regions produce. In such settings, standard log-transformations and simple dummies can lead to unstable coefficients or unintuitive signs. Some common approaches are:

• Two-part (hurdle) model: first model the probability of producing cement (producer vs. non-producer), then model production intensity and spillovers only for producers.
• Transformations: use log(x+1) or inverse hyperbolic sine (IHS) to handle zeros smoothly.
• Avoid overlapping variables: if dummy + continuous variable create collinearity, it is often better to keep just one transformed variable.
• Robustness check: run the model only on producer regions to confirm the direction of effects.

In practice, most researchers either use a two-part framework or a transformation like log(x+1) to handle the zeros, instead of including a separate dummy.

Sara Haghbayan Thank you for your response. Actually, I have tried this transformations, but they have not helped much. For instance, skewness leves decreases very slightly, distribution becomes again highly skewed. The coefficient also is not stable.

Following Sara Haghbayan's suggestions, you can also try a zero-inflated negative binomial regression model, which is a mixture model rather than a hurdle model.

Sara Haghbayan , I actually did with log (x+1) transformation and for now I will keep it as it is. My dependent variable is log (y) transformation, so do you know what is the common way of interpretation of the coefficients? Do you know any applied paper that used this kind of transformation in explanatory variable so that I can look at the paper. I know percentage to percentage transformation will not work, and interpretation depends on the amount, so I am curious how authors interpret coefficients?