The article explores how to estimate coefficients in a dynamic regression model with a unit root. By using mathematical approximations and simulations, the researchers found that accurate estimations are possible when the model includes certain types of explanatory variables. Surprisingly, different mathematical techniques gave similar results, unlike in stable regression models. When dealing with a random walk with drift model, traditional approximations were not effective for small drift values. However, a new method called small-drift asymptotics proved to be very accurate, especially with limited data.