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In my model I include the variables deposits, first at levels but after I transform them to growth rates, using $DGR=\frac{DL_2-DL_1}{DL_1}$. I have also included the exchange rate, which I have log-transformed using logarithm. Is this logic presentation of the variables? What does the log-transformed exchanged rate present? Or should I also log-transform the level of the deposits, instead of using growth rates?

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By taking the natural log of x, exchange rates, and do not log-transform y, deposits, the beta coefficient resulting from this regression indicates that a 1% change in x leads to a (beta/100) change in y. If you take the natural log of both x and y, then the beta coefficient in the regression becomes an elasticity where a 1% change in x drives a corresponding % change in y as a function of the value of beta.

Do you have other information, features or variables to include as explanatory factors in the model? For instance, if this information has been gathered over time, then including temporal factors would adjust the betas for temporal variability. What about other components such as cross-sections, e.g., countries, etc.? Then, your model would become a type of panel data model where information is pooled across the cross-sections and time, resulting in smaller errors.

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