In my opinion it cant take negative value. Lagged debt variable dosenot make any sence. there will be any debt or not so it may take either positive or zero value. most of the time it take positive value because debt increases the capital.

Oliveira, the variables are usually in ratios and they are continuous variables (similar to your growth rate type). The target debt is not observable but researchers usually express the target debt as a function of firm-specific variables and other macroeconomic variables, among others. The lagged debt ratio is also included as function or determinant of the target debt.

By definition the debt ratio should be constrained between zero and one. However, if you are using it as an independent variable in a regression, its coefficient, among other things, will depend on the dependent variable, other independent variables in the model, and the nature of the data set you are using. My advice will be that you should carefully conduct some preliminary analysis on your data set before imposing a conclusion on the regression coefficient result.

The answer is yes it can have a negative sign.  From our research using dynamic regressions such as Nguyen, Tuan; Locke, Stuart; Reddy, Krishna (2014), A dynamic estimation of governance structures and financial performance for Singaporean companies, Economic Modelling, 40, 1-11 we have struck such an interesting finding.

A negative sign indicates an inverse relationship.  If the current period has a positive relationship and the prior period a negative relationship then the explanation would lie in the adjustments in debt level that is going on.  Can the argument be made the gearing has been too low to achieve the growth in performance expected?  I think you may have an unusual finding that warrants some good thinking through and as positivists we should let the data talk not try and rule it out as it doesn’t fit a preconception.  However, you need to check your coding carefully and data to be sure something silly hasn’t happened before publishing the story.

Prof. Stuart Locke, thank you for your answer. I have come across a study that report negative coefficient on the lagged debt ratios but the authors are silent on the interpretation. I suspect that they find it hard to interpret but it is possible for the coefficient to be negative as you also noted.  Although, such results are uncommon in the literature.

Yes it can be.

refer to my article on quantcorpfin blog.

Yes, it can be. Although, findings are hard to interpret. Prof. Stuart Locke, thank you for sharing the reference.