I would like to know if there a simple way to compute coefficients for a regression in levels after having estimated a regression in first differences.
Having estimated
$$ y_t - y_{t-1} = a + b(x_t-x_{t-1}) + e_t $$
I would like to know whether I can obtain an indication of what the implied coefficients would be for the model
$$ y_t = c + dx_t + u_t $$
I personally wonder if the question makes sense but having an indication of the coefficients for the equation in levels implied by the coefficient of the equation in first differences would be very helpful to compare our results with those of other papers.
I have seen this post Fitted values from regression on first differences but I am interested in the coefficients rater than the predicted values.
